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1
Dereudre, David, and Sylvie Roelly. "Path-dependent infinite-dimensional SDE with non-regular drift : an existence result." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7208/.
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We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the
specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
2
McKinley, Scott Alister. "An existence result from the theory of fluctuating hydrodynamics of polymers in dilute solution." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1149020682.
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Orecchia, Giulio. "A monodromy criterion for existence of Néron models and a result on semi-factoriality." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0017/document.
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Cette thèse est divisée en deux parties. Dans la première partie, nous introduisons une nouvelle condition, appelée additivité torique, sur une famille de variétés abéliennes qui dégénèrent en un schéma semi-abelien au-dessus d’un diviseur à croisements normaux. La condition ne dépend que du module de Tate T l A(K sep ) de la fibre générique. Nous montrons que l’additivité torique est une condition suffisante pour l’existence d’un modèle de Néron, si la base est un schéma de caractéristique nulle. Dans le cas de la jacobienne d’une courbe lisse à réduction semi-stable, on obtient le même résultat sans aucune hypothèse sur la caractéristique de base; et nous montrons que l’additivité torique est aussi nécessaire pour l’existence d’un modèle de Néron, si la base est un schéma de caractéristique nulle. Dans la deuxième partie, on considère le cas d’une famille de courbes nodales sur un anneau de valuation discrète. On donne une condition combinatoire sur le graphe dual de la fibre spéciale, appelée semi-factorialité, qui équivaut au fait que tous les faisceaux inversibles sur la fibre générique s’étendent en des faisceaux inversibles sur l’espace total de la courbe. Il est démontré par la suite que cette condition est automatiquement satisfaite après un éclatement centré aux points fermés non-réguliers de la famille de courbes. On applique le résultat ci-dessus pour généraliser un théorème de Raynaud sur le modèle de Néron des jacobiennes de courbes lisses, au cas des courbes nodales<br>This thesis is subdivided in two parts. In the first part, we introduce a new condition, called toric-additivity, on a family of abelian varieties degenerating to a semi-abelian scheme over a normal crossing divisor. The condition depends only on the Tate module TlA(Ksep) of the generic fibre, for a prime l invertible on the base. We show that toric-additivity is a sufficient condition for the existence of a Néron model if the base is a Q-scheme. In the case of the jacobian of a smooth curve with semi-stable reduction, we obtain the same result without assumptions on the base characteristic; and we show that toric-additivity is also necessary for the existence of a Néron model, when the base is a Q-scheme. In the second part, we consider the case of a family of nodal curves over a discrete valuation ring, having split singularities. We say that such a family is semi factorial if every line bundle on the generic fibre extends to a line bundle on the total space. We give a necessary and sufficient condition for semi- factoriality, in terms of combinatorics of the dual graph of the special fibre. In particular, we show that performing one blow-up with center the non regular closed points yields a semi-factorial model of the generic fibre. As an application, we extend the result of Raynaud relating Néron models of smooth curves and Picard functors of their regular models to the case of nodal curves having a semi-factorial model
4
Roelly, Sylvie, and Pra Paolo Dai. "An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2006/668/.
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We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by
space-time cluster expansions in the small coupling parameter.
5
Ali, Zakaria Idriss. "Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth." Diss., University of Pretoria, 2010. http://hdl.handle.net/2263/29519.
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In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an existence result for such type of stochastic differential equations with non-standard growth conditions. The main difficulty in the present problem is that the existence cannot be easily retrieved from the well known results under Lipschitz type of growth conditions [42].<br>Dissertation (MSc)--University of Pretoria, 2010.<br>Mathematics and Applied Mathematics<br>unrestricted
6
Moreno-Bromberg, Santiago. "Optimal design of over-the-counter derivatives in a principal-agent framework : an existence result and numerical implementations." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/5300.
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This work lies in the intersection of Mathematical Finance, Mathematical
Economics and Convex Analysis. In terms of the latter, a new result (to the
author’s knowledge) on a Lipschitz property of the derivatives of a convex
function is presented in the first chapter. An important result on its own,
it might also provide a stepping stone to an extension to Hubert spaces of
Alexandrov’s theorem on the second derivatives of convex functions.
The second chapter considers the problem of Adverse Selection and op
timal derivative design within a Principal-Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from
weather or climate phenomena. She evaluates her risk using a coherent and
law invariant risk measure and tries to minimize her exposure by selling
derivative securities on her income to individual agents. The agents have
mean-variance preferences with heterogeneous risk aversion coefficients. An
agent’s degree of risk aversion is private information and the principal only
knows their overall distribution. It is shown that the principal’s risk mini
mization problem has a solution and, in terms of the pricing schedule, the
latter is unique.
Finding a solution to the principal’s problem requires solving a varia
tional problem with global convexity constraints. In general, this cannot be
done in closed form. To this end an algorithm to approximate the solutions
to variational problems where set of admissible functions consists of convex
functions is presented in the fourth chapter of this work. Several examples
are provided.
7
Franceschiello, Benedetta. "Mean curvature flow in SE (2) and applications to visual perception." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6959/.
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Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.
8
Murillo, Kelly Patricia. "Existence results for elliptic equations with singular terms." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/9888.
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Doutoramento em Matemática e Aplicações<br>Esta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de
equações que envolve o operador Laplaciano, um termo singular e nãolinearidade
com o exponente crítico de Sobolev, (II) uma classe de equações
com singularidade dupla, o expoente crítico de Hardy-Sobolev e um termo
côncavo e (III) uma classe de equações em forma divergente, que envolve um
termo singular, um operador do tipo Leray-Lions, e uma função definida nos
espaços de Lorentz.
As não-linearidades consideradas nos problemas (I) e (II), apresentam
dificuldades adicionais, tais como uma singularidade forte no ponto zero (de
modo que um "blow-up" pode ocorrer) e a falta de compacidade, devido à
presença do exponente crítico de Sobolev (problema (I)) e Hardy-Sobolev
(problema (II)). Pela singularidade existente no problema (III), a definição
padrão de solução fraca pode não fazer sentido, por isso, é introduzida uma
noção especial de solução fraca em subconjuntos abertos do domínio.
Métodos variacionais e técnicas da Teoria de Pontos Críticos são usados para
provar a existência de soluções nos dois primeiros problemas. No problema (I),
são usadas uma combinação adequada de técnicas de Nehari, o princípio
variacional de Ekeland, métodos de minimax, um argumento de translação e
estimativas integrais do nível de energia. Neste caso, demonstramos a
existência de (pelo menos) quatro soluções não triviais onde pelo menos uma
delas muda de sinal. No problema (II), usando o método de concentração de
compacidade e o teorema de passagem de montanha, demostramos a
existência de pelo menos duas soluções positivas e pelo menos um par de
soluções com mudança de sinal. A abordagem do problema (III) combina um
resultado de surjectividade para operadores monótonos, coercivos e
radialmente contínuos com propriedades especiais do operador de tipo Leray-
Lions. Demonstramos assim a existência de pelo menos, uma solução no
espaço de Lorentz e obtemos uma estimativa para esta solução.<br>This dissertation study mainly three elliptical problems: (I) a class of equations,
which involves the Laplacian operator, a singular term and a nonlinearity with
the critical Sobolev exponent, (II) a class of equations with double singularity,
the critical Hardy-Sobolev exponent and a concave term and (III) a class of
equations in divergent form, which involves a singular term, a Leray-Lions
operator, and a function defined on Lorentz spaces.
The nonlinearities considered in problems (I) and (II), bring additional difficulties
which, as the strong singularity at zero (so blow-up may occur) and the lack of
compactness due to the presence of a Sobolev critical exponent (problem (I))
and a Hardy-Sobolev critical exponent (problem (II)). In problem (III), the
singularity implies that the standard definition of weak solution may not make
sense. Therefore is necessary to introduce a special notion of weak solution on
open subsets of the domain.
Variational methods and Critical Point Theory techniques are used to prove the
existence of solutions in the two first problems. In problem (I), our method
combines Nehari's techniques, Ekeland's variational principle, minimax
methods, a translation argument and integral estimates of the energy level. In
this case, we prove the existence of (at least) four nontrivial solutions where at
least one of them is sign-changing. In problem (II), we prove the existence of at
least two positive solutions and a pair of sign-changing solutions, using the
concentration-compactness method and the mountain pass theorem. The
approach in problem (III) combines a surjectivity result for monotone, coercive
and radially continuous operators with special properties of Leray-Lions
operators. We prove the existence of at least one solution in a Lorentz space
and obtain an estimative for the solution.
9
Velichkov, Bozhidar. "Existence and regularity results for some shape optimization problems." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM088/document.
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Les problèmes d'optimisation de forme sont présents naturellement en physique, ingénierie, biologie, etc. Ils visent à répondre à différentes questions telles que:-A quoi une aile d'avion parfaite pourrait ressembler?-Comment faire pour réduire la résistance d'un objet en mouvement dans un gaz ou un fluide?-Comment construire une structure élastique de rigidité maximale?-Quel est le comportement d'un système de cellules en interaction?Pour des exemples précis et autres applications de l'optimisation de forme nous renvoyons à [20] et [69]. Ici, nous traitons les aspects mathématiques théoriques de l'optimisation de forme, concernant l'existence d'ensembles optimaux ainsi que leur régularité. Dans toutes les situations que l'on considère, la fonctionnelle dépend de la solution d'une certaine équation aux dérivées partielles posée sur la forme inconnue. Nous allons parfois se référer à cette fonction comme une fonction d'état.Les fonctions d'état les plus simples, mais qui apparaissent dans beaucoup de problèmes, sont données par les solutions des équations -Δw = 1 et -Δu = λu,qui sont liées à la torsion et aux modes d'oscillation d'un objet donné. Notre étude se concentrera principalement sur ces fonctionnelles de formes, impliquant la torsion et le spectre.[20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005<br>The shape optimization problems naturally appear in engineering and biology. They aim to answer questions as:-What a perfect wing may look like?-How to minimize the resistance of a moving object in a gas or a fluid?-How to build a rod of maximal rigidity?-What is the behaviour of a system of cells?The shape optimization appears also in physics, mainly in electrodynamics and in the systems presenting both classical and quantum mechanics behaviour. For explicit examples and furtheraccount on the applications of the shape optimization we refer to the books [20] and [69]. Here we deal with the theoretical mathematical aspects of the shape optimization, concerning existence of optimal sets and their regularity. In all the practical situations above, the shape of the object in study is determined by a functional depending on the solution of a given partial differential equation. We will sometimes refer to this function as a state function.The simplest state functions are provided by solutions of the equations−∆w = 1 and −∆u = λu,which usually represent the torsion rigidity and the oscillation modes of a given object. Thus our study will be concentrated mainly on the situations, in which these state functions appear,i.e. when the optimality is intended with respect to energy and spectral functionals. [20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005
10
Fialho, João Manuel Ferrão. "Existence, localization and multiplicity results for nonlinear and functional." Doctoral thesis, Universidade de Évora, 2012. http://hdl.handle.net/10174/15248.
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In this thesis several problems are addressed. The problems considered vary
from second order problems up to high order problems where generaliza-
tions to nth order are studied. Such problems range from problems without
functional dependence up to problems where the functional dependence is
featured both in the equation and on the boundary conditions.
Functional boundary conditions include most of the classical conditions
as multipoint cases, conditions with delay and/or advances, nonlocal or in-
tegral, with maximum or minimum arguments,... Existence, nonexistence,
multiplicity and localization results are then discussed in accordance with
these conditions.
The method used is the lower and upper solutions combined with di¤erent
techniques (degree theory, Nagumo condition, iterative technique, Green s
function) to obtain such results.
Several applications are studied such as the periodic oscillations of the
axis of a satellite and conjugate boundary value problems, to emphasize the
applicability of the method used; RESUMO:Nesta tese, intitulada em português, Resultados de existência, localiza-
ção e multiplicidade para problemas não lineares e funcionais de ordem su-
perior com valores na fronteira , diferentes problemas são abordados. Estes
problemas variam desde problemas de segunda ordem até problemas de or-
dem superior, onde generalizações de ordem n são feitas e onde os problemas
apresentados variam desde o caso em que não existe dependência funcional
até aos em que esta dependência funcional está presente tanto na equação
como nas condições de fronteira.
Sobre estas condições, que incluem a maioria das condições clássicas, re-
sultados de existência, não existência, multiplicidade e localização de solução
são discutidos de acordo com estas condições.
O método utilizado é o método da sub e sobre-solução combinado com
diferentes técnicas.
Várias aplicações são estudadas, nomeadamente as oscilações periódicas
do eixo de um satélite e problemas conjugados, de forma a dar ênfase à
aplicabilidade do método utilizado.
11
Kühn, Franziska. "Probability and Heat Kernel Estimates for Lévy(-Type) Processes." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-214839.
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In this thesis, we present a new existence result for Lévy-type processes. Lévy-type processes behave locally like a Lévy process, but the Lévy triplet may depend on the current position of the process. They can be characterized by their so-called symbol; this is the analogue of the characteristic exponent in the Lévy case. Using a parametrix construction, we prove the existence of Lévy-type processes with a given symbol under weak regularity assumptions on the regularity of the symbol. Applications range from existence results for stable-like processes and mixed processes to uniqueness results for Lévy-driven stochastic differential equations.
Moreover, we discuss sufficient conditions for the existence of moments of Lévy-type processes and derive estimates for fractional moments.
12
Manicom, Gray Thomas. "Existence results for a class of semi-linear initial value problems." Diss., University of Pretoria, 2017. http://hdl.handle.net/2263/63288.
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The main result of this thesis is an existence result for parabolic semi-linear
problems. This is done by reformulating the semi-linear problem as an abstract
Cauchy problem
ut(t) = Au(t) + f(t; u(t)), t > 0
u(0) = u0 (1)
for u0 2 X, where X is a Banach space. We then develop and use the theory
of compact semigroups to prove an existence result.
In order to make this result applicable, we give a characterization of
compact semigroups in terms of its resolvent operator and continuity in the
uniform operator topology. Thus, using the theory of analytic semigroups,
we are able to determine under what conditions on A a solution to (1) exists.
Furthermore, we consider the asymptotic behaviour and regularity of such
solutions. By developing perturbation theory, we are easily able to apply our
existence result to a larger class of problems. We then demonstrate these
results with an example.
This work is signi cant in providing a novel approach to a group of previously
established results. The content can be considered pure mathematics,
but it is of signi cant importance in real world situations. The structure
of the thesis, and the choice of certain de nitions, lends itself to be easily
understood and interpreted in the light of these real world situations and
is intended to be easily followed by an applied mathematician. An important
part of this process is to develop the problem in a real Hilbert space
and then to consider the complexi cation of the problem in order to reset
it in a complex Hilbert space, in which we can apply the theory of analytic
semigroups. A large number of real world problems fall into the class of
problems discussed here, not only in biology as demonstrated, but also in
physics, chemistry, and elsewhere.<br>Dissertation (MSc)--University of Pretoria, 2017.<br>Mathematics and Applied Mathematics<br>MSc<br>Unrestricted
13
Sauer, Martin [Verfasser]. "Existence and Uniqueness Results for Randomly Forced Generalized Newtonian Fluids / Martin Sauer." München : Verlag Dr. Hut, 2013. http://d-nb.info/1034003283/34.
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Meinert, Melissa [Verfasser]. "Partial differential equations on fractals. Existence, Uniqueness and Approximation results / Melissa Meinert." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1214806538/34.
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Nerlich, Alexander [Verfasser]. "Adding randomness to nonlinear semigroups: existence, uniqueness and asymptotic results / Alexander Nerlich." Ulm : Universität Ulm, 2018. http://d-nb.info/1171900880/34.
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Luo, Yongming [Verfasser]. "Existence and Regularity Results of a Ferroelectric Phase-Field Model / Yongming Luo." Kassel : Universitätsbibliothek Kassel, 2019. http://d-nb.info/1201508339/34.
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Hebestreit, Niklas [Verfasser], Christiane [Gutachter] Tammer, and Franco [Gutachter] Giannessi. "Existence results for vector quasi-variational problems / Niklas Hebestreit ; Gutachter: Christiane Tammer, Franco Giannessi." Halle (Saale) : Universitäts- und Landesbibliothek Sachsen-Anhalt, 2020. http://d-nb.info/122159981X/34.
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Araújo, Yane Lísley Ramos. "Existence results for some elliptic equations involving the fractional Laplacian operator and critical growth." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9252.
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Previous issue date: 2015-12-18<br>In this work we prove some results of existence and multiplicity of solutions for equations
of the type
( ) u + V (x)u = f(x; u) in RN;
where 0 < < 1, N 2 , ( ) denotes the fractional Laplacian, V : RN ! R is a
continuous function that satisfy suitable conditions and f : RN R ! R is a continuous
function that may have critical growth in the sense of the Trudinger-Moser inequality
or in the sense of the critical Sobolev exponent. In order to obtain our results we
use variational methods combined with a version of the Concentration-Compactness
Principle due to Lions.<br>Neste trabalho provamos alguns resultados de existência e multiplicidade de soluções
para equações do tipo
( ) u + V (x)u = f(x; u) em RN;
onde 0 < < 1, N 2 , ( ) denota o Laplaciano fracionário, V : RN ! R é uma
função contínua que satisfaz adequadas condições e f : RN R ! R é uma função cont
ínua que pode ter crescimento crítico no sentido da desigualdade de Trudinger-Moser
ou no sentido do expoente crítico de Sobolev. A m de obter nossos resultados usamos
métodos variacionais combinados com uma versão do Princípio de Concentração-
Compacidade devido à Lions.
19
Cabarrubias, Bituin C. "Existence, uniqueness and homogenization results for a class of nonlinear PDE in perforated domains." Rouen, 2012. http://www.theses.fr/2012ROUES046.
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This thesis is devoted to the existence, uniqueness and homogenization results for a quasilinear elliptic problem with oscillating coefficients and with nonlinear Robin boundary condition in a periodically perforated domain. A suitable frowth conditions are assumed on the nonlinear boundary term and on the quasilinear term, some assumptions on the modulus of continuity introduced in Chipot [17] and weaker than a Lipschitz condition, are prescribed. For the existence and uniqueness of a solution, we consider a more general framework which, in particular, will imply the existence and uniqueness of the solution of the problem. To deal with the existence of a solution, we prove first the weak continuity of the boundary nonlinear operator which is a difficult part. Together with this property, we use the Schauder's Fixed Point Theorem to show the existence. For the uniqueness, we adapt to our situation some arguments introduced in André-Chipot [5] (see also chapter 11 of [17] for Dirichlet conditions) and partially extended to linear Robin conditions in Bendib-Tcheugoué Tébou [11] and Bendib [10]. For the homogenization of the problem, we study the convergence to a limit problem using the Periodic Unfolding Method in perforated domains. Here, we proved related properties of the onfolding operators which are needed in the process. We also show the well-posedness of the limit system by proving that the homogenized operator inherits the modulus of continuity of the initial problem. As a consequence, the uniqueness of a solution of the homogenized quasilinear problem follows. A corrector result is also obtained using this method.
20
Tian, Rushun. "Existence and Multiplicity Results on Standing Wave Solutions of Some Coupled Nonlinear Schrodinger Equations." DigitalCommons@USU, 2013. https://digitalcommons.usu.edu/etd/1484.
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Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods.
Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational structure. For such an equation or system, a weak solution can be found through finding the critical point of a corresponding energy functional. If this equation or system is also invariant under a certain symmetric group, multiple solutions are often expected. In this work, an integer-valued function that measures symmetries of CNLS was used to determine critical values. Besides variational methods, bifurcation methods may also be used to find solutions of a differential equation or system, if some trivial solution branch exists and the system is degenerate somewhere on this branch. If local bifurcations exist, then new solutions can be found in a neighborhood of each bifurcation point. If global bifurcation branches exist, then there is a continuous solution branch emanating from each bifurcation point.
We consider two types of CNLS. First, for a fully symmetric system, we introduce a new index and use it to construct a sequence of critical energy levels. Using variational methods and the symmetric structure, we prove that there is at least one solution on each one of these critical energy levels. Second, we study the bifurcation phenomena of a two-equation asymmetric system. All these bifurcations take place with respect to a positive solution branch that is already known. The locations of the bifurcation points are determined through an equation of a coupling parameter. A few nonexistence results of positive solutions are also given
21
Yusuf, Owolabi. "On models of Kirchhoff Equations with damping terms: existence results and asymptotic behaviour of solutions." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29370.
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Azizieh, Céline. "A priori estimates, continuation methods and existence results for positive solutions of p-Laplace eauqations and systems." Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211660.
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Mazzoleni, Dario [Verfasser], Aldo [Akademischer Betreuer] Pratelli, Dorin [Akademischer Betreuer] Bucur, and Giuseppe [Akademischer Betreuer] Buttazzo. "Existence and regularity results for solutions of spectral problems / Dario Mazzoleni. Gutachter: Aldo Pratelli ; Dorin Bucur ; Giuseppe Buttazzo." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://d-nb.info/1065270380/34.
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Schätzler, Leah [Verfasser], Frank [Akademischer Betreuer] Duzaar, and Frank [Gutachter] Duzaar. "Existence and Stability Results for Nonlinear and Doubly Nonlinear Evolutionary Problems / Leah Schätzler ; Gutachter: Frank Duzaar ; Betreuer: Frank Duzaar." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020. http://d-nb.info/1216704287/34.
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Hauser, Carlos [Verfasser], and W. [Akademischer Betreuer] Reichel. "Existence Results and A Priori Bounds for Positive Solutions of Discrete Nonlinear Elliptic Equations / Carlos Hauser ; Betreuer: W. Reichel." Karlsruhe : KIT-Bibliothek, 2019. http://d-nb.info/1190178923/34.
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Herán, Andreas [Verfasser], Jens [Akademischer Betreuer] Habermann, and Jens [Gutachter] Habermann. "Existence and Regularity Results for Parabolic Problems on Metric Measure Spaces / Andreas Herán ; Gutachter: Jens Habermann ; Betreuer: Jens Habermann." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020. http://d-nb.info/1218785721/34.
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Huang, Lirong. "Multiplicity results for some classes of Schrödinger-Poisson systems." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12867.
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Doutoramento conjunto em Matemática - Matemática e Aplicações (PDMA)<br>In this thesis, we study the existence and multiplicity of solutions of the
following class of Schr odinger-Poisson systems:
u + u + l(x) u = (x; u) in R3;
= l(x)u2 in R3;
where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity
satis es the following three kinds of cases:
(i) a subcritical exponent with (x; u) = k(x)jujp2u + h(x)u (4 p <
2 ) under an inde nite case;
(ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u;
(iii) a critical growth exponent with (x; u) = k(x)juj2 2u +
h(x)jujq2u (2 q < 2 ).
It is worth mentioning that the thesis contains three main innovations except
overcoming several di culties, which are generated by the systems themselves.
First, as an unknown referee said in his report, we are the rst authors
concerning the existence of multiple positive solutions for Schr odinger-
Poisson systems with an inde nite nonlinearity.
Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3
that we do not need the condition
R
R3 k(x)ep
1dx < 0 with an inde nite noncoercive
case, where e1 is the rst eigenfunction of +id in H1(R3) with
weight function h. A similar condition has been shown to be a su cient
and necessary condition to the existence of positive solutions for semilinear
elliptic equations with inde nite nonlinearity for a bounded domain (see
e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be
a su cient condition to the existence of positive solutions for semilinear
elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani,
Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in
this case can be applied to study other aspects of the Schr odinger-Poisson
systems and it gives a way to study the Kirchho system and quasilinear
Schr odinger system.
Finally, to get sign changing solutions in Chapter 5, we follow the spirit of
Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but
the procedure is simpler than that they have proposed in their paper.<br>Nesta tese, estudamos a existência e a multiplicidade de soluções da seguinte
classe de sistemas denominada de Schr odinger-Poisson:
u + u + l(x) u = (x; u) in R3;
= l(x)u2 in R3; onde l 2 L2(R3) ou l 2 L1(R3). Consideram-se não-linearidades que
satisfazem um dos seguintes casos:
(i) potências que envolvem um expoente sub-cr tico, da forma (x; u) =
k(x)jujp2u + h(x)u, (4 p < 2 ), sendo k uma função com sinal
indefinido e h uma função positiva;
(ii) caso geral de uma não-linearidade indefi nida, da forma (x; u) =
k(x)g(u) + h(x)u, sendo k uma função com sinal indefinido e h uma função positiva;
(iii) potências que envolvem o expoente crí tico, da forma (x; u) =
k(x)juj2 2u + h(x)jujq2u (2 q < 2 ).
Convém salientar que esta tese tem três principais inovações, as quais
ultrapassam dificuldades geradas pela natureza dos problemas estudados.
Primeiro, como um relator anónimo referiu, este é o primeiro trabalho em
que se trata a existência de várias soluções de sistemas de Schrödinger-
Poisson com não-linearidade indefinida.
Segundo, neste estudo encontrou-se um fen ómeno interessante, ver
Capítulos 2 e 3, nomeadamente, não ser necess ária a condição R3 k(x)ep
1dx < 0 no caso indefinido e não-coercivo, sendo e1 a função
associada ao primeiro valor próprio de + id em H1(R3) com peso
h. Note-se que foi demonstrado que uma condi cão semelhante e condição
necessária e suficiente na existência de solu cões positivas para equações
elíticas semilineares com não-linearidades indefinidas em domínios limitados
(ver e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475),
ou ser uma condição suficiente na existência de soluções positivas para
equações elíticas semilineares com não-linearidades indefinidas em RN (see
e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Adicionalmente, o método utilizado pode ser utilizado para estudar outros aspetos dos sistemas de Schrodinger-Poisson, permite também estudar sistemas de
Kirchho e sistemas de Schrodinger quasilineares.
Por m, para obter soluções com mudança de sinal no Cap. 5, segue se
a ideia de Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137
(2007), 333, mas o método utilizado é uma versão simplificada do método
apresentado no artigo referido.
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Piovano, Paulo. "Evolution and Regularity Results for Epitaxially Strained Thin Films and Material Voids." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/96.
Full textAbstract:
In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy.
First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity.
Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.
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Palmieri, Alessandro [Verfasser], Michael [Akademischer Betreuer] Reissig, Michael [Gutachter] Reissig, and Vladimir [Gutachter] Georgiev. "Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass / Alessandro Palmieri ; Gutachter: Michael Reissig, Vladimir Georgiev ; Betreuer: Michael Reissig." Freiberg : Technische Universität Bergakademie Freiberg, 2018. http://d-nb.info/1226100945/34.
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Westergren, Gisela. "Om jag inte kan göra nog så gör jag istället ingenting." Thesis, Konstfack, Ädellab, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:konstfack:diva-6259.
Full textAbstract:
It`s blameful to do nothing. You should catch the day and its possibilities. Every second, minute and day, you have the potential to be constantly productive. Do not lose a second of time that you can use to create an imprint of your existence. Do not waste your time when you have the opportunity to create something measurably valuable. Soon you are gone and the competition is great. Doing nothing is a task that fewer and fewer are devoted to, to a lesser extent. We are expected to always be accessible and keep up to date with what is happening around us. There is a constant occupation of our sense of mind, thoughtfulness and rest is unprioritized. We try to maximize the part of our time when we are productive and active to absurdity. The goal seems to make as big imprint of our existence as possible. Fast and more is applauded until the day we burn ourselves out. In my work, I investigate passivity as backlash in a faster world, in a world where focus is on production, efficiency and results. A world where everything worth valuing is measurable. What is really a desired result and is it always possible to measure? Who really gets that gain from our fast life? Can passivity and slowness act as an activist act? Can one passively create something measurable? Is burning time perhaps our time´s most provocative act? With my work, I want to question my constant bad conscience about being insufficient and my feeling of not doing enough. If I can´t do enough, I do nothing instead.<br>Det är skuldbelagt att göra ingenting. Du bör fånga dagen och dess möjligheter. Varje sekund, minut och dag har du potential att vara konstant produktiv. Förlora inte en sekund av tid som du kan använda till att skapa ett avtryck av din existens. Slösa inte med din tid när du har möjlighet att skapa något mätbart värdefullt. Snart är du borta och konkurrensen är stor. Att göra ingenting är en syssla som allt färre ägnar sig åt. Vi förväntas alltid vara tillgängliga och hålla oss uppdaterade om vad som händer runt oss. Det sker ständigt en ockupation av våra sinnesintryck. Eftertänksamhet och vila prioriteras bort. Vi försöker att maximera den del av vår tid då vi är produktiva och aktiva till absurditet. Målet verkar vara att hinna sätta ett så stort avtryck av vår existens som möjligt. Snabbare och mer applåderas till den dagen då vi bränner ut oss. I mitt arbete undersöker jag passivitet som motreaktion till en snabbare värld, i en värld där fokus ligger på produktion, effektivitet och resultat. I en värld där endast det som är mätbart ges ett värde. Vad är egentligen ett önskat resultat och är det alltid möjligt att mäta? Vem är det egentligen som får vinsten av vårt snabba liv? Kan passivitet och långsamhet fungera som en aktivistisk handling? Kan man passivt skapa något mätbart? Är ”att bränna tid” kanske vår tids mest provokativa handling? Med mitt arbete vill jag ifrågasätta mitt konstanta dåliga samvete om att vara otillräcklig och min känsla av att jag inte gör tillräckligt. Om jag inte kan göra nog så gör jag istället ingenting.
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Bourdin, Loïc. "Contributions au calcul des variations et au principe du maximum de Pontryagin en calculs time scale et fractionnaire." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3009/document.
Full textAbstract:
Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin (PMP en abrégé) pour des problèmes de contrôle optimal. Dans ce but, nous généralisons plusieurs méthodes variationnelles usuelles, allant du simple calcul des variations au principe variationnel d’Ekeland (couplé avec la technique des variations-aiguilles), en passant par l’étude d’invariances variationnelles par des groupes de transformations. Les démonstrations des PMPs nous amènent également à employer des théorèmes de point fixe et à prendre en considération la technique des multiplicateurs de Lagrange ou encore une méthode basée sur un théorème d’inversion locale conique. Ce manuscrit est donc composé de deux parties : la Partie 1 traite de problèmes variationnels posés sur time scale et la Partie 2 est consacrée à leurs pendants fractionnaires. Dans chacune de ces deux parties, nous suivons l’organisation suivante : 1. détermination de l’équation d’Euler-Lagrange caractérisant les points critiques d’une fonctionnelle Lagrangienne ; 2. énoncé d’un théorème de type Noether assurant l’existence d’une constante de mouvement pour les équations d’Euler-Lagrange admettant une symétrie ; 3. énoncé d’un théorème de type Tonelli assurant l’existence d’un minimiseur pour une fonctionnelle Lagrangienne et donc, par la même occasion, d’une solution pour l’équation d’Euler-Lagrange associée (uniquement en Partie 2) ; 4. énoncé d’un PMP (version forte en Partie 1, version faible en Partie 2) donnant une condition nécessaire pour les trajectoires qui sont solutions de problèmes de contrôle optimal généraux non-linéaires ; 5. détermination d’une condition de type Helmholtz caractérisant les équations provenant d’un calcul des variations (uniquement en Partie 1 et uniquement dans les cas purement continu et purement discret). Des théorèmes de type Cauchy-Lipschitz nécessaires à l’étude de problèmes de contrôle optimal sont démontrés en Annexe<br>This dissertation deals with the mathematical fields called calculus of variations and optimal control theory. More precisely, we develop some aspects of these two domains in discrete, more generally time scale, and fractional frameworks. Indeed, these two settings have recently experience a significant development due to its applications in computing for the first one and to its emergence in physical contexts of anomalous diffusion for the second one. In both frameworks, our goals are: a) to develop a calculus of variations and extend some classical results (see below); b) to state a Pontryagin maximum principle (denoted in short PMP) for optimal control problems. Towards these purposes, we generalize several classical variational methods, including the Ekeland’s variational principle (combined with needle-like variations) as well as variational invariances via the action of groups of transformations. Furthermore, the investigations for PMPs lead us to use fixed point theorems and to consider the Lagrange multiplier technique and a method based on a conic implicit function theorem. This manuscript is made up of two parts : Part A deals with variational problems on time scale and Part B is devoted to their fractional analogues. In each of these parts, we follow (with minor differences) the following organization: 1. obtaining of an Euler-Lagrange equation characterizing the critical points of a Lagrangian functional; 2. statement of a Noether-type theorem ensuring the existence of a constant of motion for Euler-Lagrange equations admitting a symmetry;3. statement of a Tonelli-type theorem ensuring the existence of a minimizer for a Lagrangian functional and, consequently, of a solution for the corresponding Euler-Lagrange equation (only in Part B); 4. statement of a PMP (strong version in Part A and weak version in Part B) giving a necessary condition for the solutions of general nonlinear optimal control problems; 5. obtaining of a Helmholtz condition characterizing the equations deriving from a calculus of variations (only in Part A and only in the purely continuous and purely discrete cases). Some Picard-Lindelöf type theorems necessary for the analysis of optimal control problems are obtained in Appendices
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Tavares, Lucas Alves. "O envolvimento da proteína adaptadora 1 (AP-1) no mecanismo de regulação negativa do receptor CD4 por Nef de HIV-1." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/17/17136/tde-06012017-113215/.
Full textAbstract:
O Vírus da Imunodeficiência Humana (HIV) é o agente etiológico da Síndrome da Imunodeficiência Adquirida (AIDS). A AIDS é uma doença de distribuição mundial, e estima-se que existam atualmente pelo menos 36,9 milhões de pessoas infectadas com o vírus. Durante o seu ciclo replicativo, o HIV promove diversas alterações na fisiologia da célula hospedeira a fim de promover sua sobrevivência e potencializar a replicação. A rápida progressão da infecção pelo HIV-1 em humanos e em modelos animais está intimamente ligada à função da proteína acessória Nef. Dentre as diversas ações de Nef está a regulação negativa de proteínas importantes na resposta imunológica, como o receptor CD4. Sabe-se que esta ação resulta da indução da degradação de CD4 em lisossomos, mas os mecanismos moleculares envolvidos ainda são totalmente elucidados. Nef forma um complexo tripartite com a cauda citosólica de CD4 e a proteína adaptadora 2 (AP-2), em vesículas revestidas por clatrina nascentes, induzindo a internalização e degradação lisossomal de CD4. Pesquisas anteriores demonstraram que o direcionamento de CD4 aos lisossomos por Nef envolve a entrada do receptor na via dos corpos multivesiculares (MVBs), por um mecanismo atípico, pois, embora não necessite da ubiquitinação de carga, depende da ação de proteínas que compõem os ESCRTs (Endosomal Sorting Complexes Required for Transport) e da ação de Alix, uma proteína acessória da maquinaria ESCRT. Já foi reportado que Nef interage com subunidades dos complexos AP-1, AP-2, AP-3 e Nef não parece interagir com subunidades de AP-4 e AP-5. Entretanto, o papel da interação de Nef com AP-1 e AP-3 na regulação negativa de CD4 ainda não está totalmente elucidado. Ademais, AP-1, AP-2 e AP-3 são potencialmente heterogêneos devido à existência de isoformas múltiplas das subunidades codificadas por diferentes genes. Todavia, existem poucos estudos para demonstrar se as diferentes combinações de isoformas dos APs são formadas e se possuem propriedades funcionais distintas. O presente trabalho procurou identificar e caracterizar fatores celulares envolvidos na regulação do tráfego intracelular de proteínas no processo de regulação negativa de CD4 induzido por Nef. Mais especificamente, este estudo buscou caracterizar a participação do complexo AP-1 na modulação negativa de CD4 por Nef de HIV-1, através do estudo funcional das duas isoformas de ?-adaptina, subunidades de AP-1. Utilizando a técnica de Pull-down demonstramos que Nef é capaz de interagir com ?2. Além disso, nossos dados de Imunoblot indicaram que a proteína ?2-adaptina, e não ?1-adaptina, é necessária no processo de degradação lisossomal de CD4 por Nef e que esta participação é conservada para degradação de CD4 por Nef de diferentes cepas virais. Ademais, por citometria de fluxo, o silenciamento de ?2, e não de ?1, compromete a diminuição dos níveis de CD4 por Nef da membrana plasmática. A análise por imunofluorêsncia indireta também revelou que a diminuição dos níveis de ?2 impede a redistribuição de CD4 por Nef para regiões perinucleares, acarretando no acúmulo de CD4, retirados por Nef da membrana plasmática, em endossomos primários. A depleção de ?1A, outra subunidade de AP-1, acarretou na diminuição dos níveis celulares de ?2 e ?1, bem como, no comprometimento da eficiente degradação de CD4 por Nef. Além disso, foi possível observar que, ao perturbar a maquinaria ESCRT via super-expressão de HRS (uma subunidade do complexo ESCRT-0), ocorreu um acumulo de ?2 em endossomos dilatados contendo HRS-GFP, nos quais também detectou-se CD4 que foi internalizado por Nef. Em conjunto, os resultados indicam que ?2-adaptina é uma importante molécula para o direcionamento de CD4 por Nef para a via ESCRT/MVB, mostrando ser uma proteína relevante no sistema endo-lisossomal. Ademais, os resultados indicaram que as isoformas ?-adaptinas não só possuem funções distintas, mas também parecem compor complexos AP-1 com diferentes funções celulares, já que apenas a variante AP-1 contendo ?2, mas não ?1, participa da regulação negativa de CD4 por Nef. Estes estudos contribuem para o melhor entendimento dos mecanismos moleculares envolvidos na atividade de Nef, que poderão também ajudar na melhor compreensão da patogênese do HIV e da síndrome relacionada. Em adição, este trabalho contribui para o entendimento de processos fundamentais da regulação do tráfego de proteínas transmembrana no sistema endo-lisossomal.<br>The Human Immunodeficiency Virus (HIV) is the etiologic agent of Acquired Immunodeficiency Syndrome (AIDS). AIDS is a disease which has a global distribution, and it is estimated that there are currently at least 36.9 million people infected with the virus. During the replication cycle, HIV promotes several changes in the physiology of the host cell to promote their survival and enhance replication. The fast progression of HIV-1 in humans and animal models is closely linked to the function of an accessory protein Nef. Among several actions of Nef, one is the most important is the down-regulation of proteins from the immune response, such as the CD4 receptor. It is known that this action causes CD4 degradation in lysosome, but the molecular mechanisms are still incompletely understood. Nef forms a tripartite complex with the cytosolic tail of the CD4 and adapter protein 2 (AP-2) in clathrin-coated vesicles, inducing CD4 internalization and lysosome degradation. Previous research has demonstrated that CD4 target to lysosomes by Nef involves targeting of this receptor to multivesicular bodies (MVBs) pathway by an atypical mechanism because, although not need charging ubiquitination, depends on the proteins from ESCRTs (Endosomal Sorting Complexes Required for Transport) machinery and the action of Alix, an accessory protein ESCRT machinery. It has been reported that Nef interacts with subunits of AP- 1, AP-2, AP-3 complexes and Nef does not appear to interact with AP-4 and AP-5 subunits. However, the role of Nef interaction with AP-1 or AP-3 in CD4 down-regulation is poorly understood. Furthermore, AP-1, AP-2 and AP-3 are potentially heterogeneous due to the existence of multiple subunits isoforms encoded by different genes. However, there are few studies to demonstrate if the different combinations of APs isoforms are form and if they have distinct functional properties. This study aim to identify and characterize cellular factors involved on CD4 down-modulation induced by Nef from HIV-1. More specifically, this study aimed to characterize the involvement of AP-1 complex in the down-regulation of CD4 by Nef HIV-1 through the functional study of the two isoforms of ?-adaptins, AP-1 subunits. By pull-down technique, we showed that Nef is able to interact with ?2. In addition, our data from immunoblots indicated that ?2- adaptin, not ?1-adaptin, is required in Nef-mediated targeting of CD4 to lysosomes and the ?2 participation in this process is conserved by Nef from different viral strains. Furthermore, by flow cytometry assay, ?2 depletion, but not ?1 depletion, compromises the reduction of surface CD4 levels induced by Nef. Immunofluorescence microscopy analysis also revealed that ?2 depletion impairs the redistribution of CD4 by Nef to juxtanuclear region, resulting in CD4 accumulation in primary endosomes. Knockdown of ?1A, another subunit of AP-1, resulted in decreased cellular levels of ?1 and ?2 and, compromising the efficient CD4 degradation by Nef. Moreover, upon artificially stabilizing ESCRT-I in early endosomes, via overexpression of HRS, internalized CD4 accumulates in enlarged HRS-GFP positive endosomes, where co-localize with ?2. Together, the results indicate that ?2-adaptin is a molecule that is essential for CD4 targeting by Nef to ESCRT/MVB pathway, being an important protein in the endo-lysosomal system. Furthermore, the results indicate that ?-adaptins isoforms not only have different functions, but also seem to compose AP-1 complex with distinct cell functions, and only the AP-1 variant comprising ?2, but not ?1, acts in the CD4 down-regulation induced by Nef. These studies contribute to a better understanding on the molecular mechanisms involved in Nef activities, which may also help to improve the understanding of the HIV pathogenesis and the related syndrome. In addition, this work contributes with the understanding of primordial process regulation on intracellular trafficking of transmembrane proteins.
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Wei, Chao-Cheng, and 魏照誠. "Existence result of mild solution of Boltzmann equation." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/07457437236445898991.
Full textAbstract:
碩士<br>國立政治大學<br>應用數學研究所<br>98<br>In this thesis, we consider the initial-value problem for the Boltzmann equation.We prove that the existence of mild solution in the weighted Lebesgue space by using Banach's fixed point theorem, and that the uniform stability of solution with respect to the weighted norm.
Key words: Boltzmann equation, Maxwellian, existence of mild solutions, uniform stability.
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Chan, Justin. "Asymptotic existence results on specific graph decompositions." Thesis, 2010. http://hdl.handle.net/1828/2909.
Full textAbstract:
This work examines various asymptotic edge-decomposition problems on graphs. A G-group divisible design (G-GDD) of type [g_1, ..., g_u] and index lambda is a decomposition of the edges of the complete lambda-fold multipartite graph H, with groups (maximal independent sets) G_1, ..., G_n, |G_i| = g_i, into graphs (blocks) isomorphic to G. We shall also examine special types of G-GDDs (such as G-frames) and prove that, given all parameters except u, these structures exist for all asymptotically large u satisfying the necessary conditions. Our primary technique is to invoke a useful theorem of Lamken and Wilson on edge-colored
graph decompositions. The basic construction for k-RGDDs shall be outlined at the end of the thesis.
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Mou, Libin H. "Some existence and uniqueness results of harmonic maps." Thesis, 1990. http://hdl.handle.net/1911/16374.
Full textAbstract:
This thesis discusses some existence and uniqueness problems of harmonic maps. It consists of two parts: Part I. Existence of harmonic maps with prescribed finite singularities. Here we address the question of existence of a harmonic map from a spatial domain to the sphere S$\sp2$ which has a prescribed finite set of singularities.
Part II. Uniqueness of energy minimizing harmonic maps for almost all smooth boundary data. Suppose $\Omega$ is a smooth domain in R$\sp{m}$ and N is a compact smooth manifold. Here we show roughly that almost all smooth maps from $\partial\Omega$ to N serve as boundary values for a unique energy minimizing map u from $\Omega$ to N. This involves constructing a finite measure on a suitable (infinite dimensional) space of smooth boundary values.
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Xu, Jia-Ren, and 許嘉仁. "Existence results of capillary surfaces over convex domains." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/47886333637563213405.
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"Ergodic control of multidimensional diffusions I. : the existence results." Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1986. http://hdl.handle.net/1721.1/2951.
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Chen, Show-Ching, and 陳秀青. "EXISTENCE RESULTS FOR HAMMERSTEIN INTEGRAL EQUATIONS AND RELATED TOPICS." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/99734197373023885880.
Full textAbstract:
碩士<br>國立台北師範學院<br>數理教育研究所<br>90<br>Abstract
We shall provide conditions on non-positive function f (t, u), the Hammerstein integral equation
and the weighted Hammerstein integral equation
have at least one solution.
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謝宗憲. "Some existence results for soluations of traveling wave type." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/31120718744331384489.
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YU, HUI-ZHEN, and 余慧真. "Existence results of strong solutions for certain quasilinear elliptic problems." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/27518013844424526130.
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Lin, Ya-Ping, and 林雅萍. "Some existence results for steady states of reaction-diffusion systems." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/93457131788327469250.
Full textAbstract:
博士<br>國立彰化師範大學<br>數學系所<br>94<br>Abstract
In this thesis, we are interested in the existence of steady states of reaction-di.usion systems with skew-gradient structure. We use two di.erent types of variational arguments to study the existence of steady states. In addition, we obtain a standing wave solution, by making use of ordered methods for quasi-monotone systems.
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Bruso, Keith Alvin. "Existence, uniqueness and blow-up results for non-linear wave equations." 1985. http://hdl.handle.net/2097/27403.
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Tiago, Jorge Filipe Duarte. "Existence results and applications for some non-linear optimal control problems." Doctoral thesis, 2009. http://hdl.handle.net/10451/1657.
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Tese de doutoramento, Matemática (Análise Matemática), 2010, Universidade de Lisboa, Faculdade de Ciências<br>Os resultados clássicos de existência, para problemas de controlo óptimo, governados por sistemas de equações diferenciais ordinárias, baseam-se em condições de convexidade que resultam frequentemente muito difíceis de verificar. Apresentamos uma abordagem geral para este problema, com base em várias relaxações do mesmo, na qual a convexidade surge de um modo inesperada. Isolamos uma condição suficiente, para a existência de soluções óptimas, que pode ser verificada em vários contextos. Podemos chegar a um resultado de existência para problemas vectoriais, com uma estrutura particular, proveniente de problemas de controlo e manobra deve veículos subaquáticos. Numa abordagem diferente, recuperamos técnicas clássicas baseadas na reformulação variacional, que nos permitem obter resultados de existência através da aplicação de teoremas para problemas variacionais, sem condições de convexidade. Em particular, provamos a existência de solução, no caso escalar, para problemas de controlo óptimo autónomos.Utilizamos o nosso resultado de existência, demonstrado para problemas de controlo óptimo com variáveis vectoriais, para provar a existência de solução para um problema de manobra de veículos subaquáticos. Para terminar, apresentamos algumas ideias para trabalho futuro. Propomos a implementação de um método numérico, baseado em direcções de descida mais rápida, para aproximar soluções de problemas de controlo óptimo vindos das aplicações. Mostramos resultados preliminares desta implementação, para alguns exemplos académicos.<br>Classical existence results for optimal control problems governed by systems of ordinary differential equations are based on typical convexity assumptions, which are quite often, very difficult to check. We present a general approach to prove existence of solutions for optimal control problems, based on several relaxations of the problem, where the convexity arises inan unexpected way. We isolate one sufficient condition for the existence of optimal solutions, which can be validated in various contexts. We end up with a main existence result for vector problems with a particular structure, motivated by underwater-vehicles-maneuvering problems. Alternatively, we recover the classical approach based on a purely variational reformulation, which can lead to existence results by using one existence theorems for variational problems without convexity assumptions. In particular we prove the existence of solution for autonomous scalar optimal control problems. Finally, we apply our existence result for vector state and control variables, to prove the local existence of solution for an optimal control problem describing the control of an underwater vehicle. Additionally to the main work described above, we introduce some ideas for future work. We propose to implement a numerical method, based on steepest descent directions, to approximate the solutions of realistic optimal control problems. Some preliminary results for academic examples are shown.<br>Fundação para a Ciência e Tecnologia (SFRH-BD-22107-2005), Programa Operacional Ciência e Inovaçao 2010
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Kim, Christina. "Uniqueness and existence results on viscosity solutions of some free boundary problems." 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3101218.
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Alpay, Mehmet Emin. "Existence and uniqueness results for ��� -optimal linear dynamic controllers for discrete time SISO systems." Thesis, 1995. http://hdl.handle.net/1957/34990.
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Seehafer, Martin [Verfasser]. "Existence results for plasma physics models containing a fully coupled magnetic field / von Martin Seehafer." 2009. http://d-nb.info/995569320/34.
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Tang, Dalin. "Peristaltic transport of a heat-conducting fluid existence, uniqueness, stability, asymptotic expansion and numerical results." 1988. http://catalog.hathitrust.org/api/volumes/oclc/19759632.html.
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Palmieri, Alessandro. "Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass." Doctoral thesis, 2018. https://tubaf.qucosa.de/id/qucosa%3A31787.
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The PhD thesis deals with global in time existence results and blow-up result for a semilinear wave model with scale-invariant damping and mass. Since the time-dependent coefficients for the considered model make somehow the damping and the mass a threshold term between effective and non-effective terms, it turns out that a fundamental role in the description of qualitative properties of solutions to this semilinear model and to the corresponding linear homogeneous Cauchy problem is played by the multiplicative constants appearing in those coefficients. For coefficients that make the damping term dominant, we can use the standard approach for the classical damped wave model with L^2 − L^2 estimates and the so-called test function method. On the other hand, when the interaction among those coefficients is balanced, then, it is possible to observe how typical tools for hyperbolic models, as for example Kato’s lemma, provide sharp global in time existence results and sharp blow-up results for super- and sub-Strauss type exponents, respectively.
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Carstens, Christoffel. "Invloed van televisie op die verwestersingsproses by die Swart adolessent." Thesis, 1995. http://hdl.handle.net/10500/16335.
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