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Dissertations / Theses on the topic 'Nonlinear PDE'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Sabra, Ahmad. "Nonlinear PDE and Optical Surfaces Design." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/345398.

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Mathematics<br>Ph.D.<br>We introduce two models to design near field reflectors in R^3 that solve an inverse problem in radiometry, taking into account the inverse square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from the source to avoid obstruction. In the second model, the reflectors are neither convex nor concave and do not block the rays even if they are close to the source.<br>Temple University--Theses

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2

Saha, Rupesh Kumar. "On some aspects of nonlinearity and role of parameters in some nonlinear PDE`s from physical origin." Thesis, University of North Bengal, 2009. http://hdl.handle.net/123456789/1372.

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3

Ching, Joshua. "Singular Solutions of Nonlinear Elliptic Equations with Gradient Terms." Thesis, The University of Sydney, 2017. http://hdl.handle.net/2123/16848.

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On punctured domains of $\mathbb{R}^N$ with $N \geq 2$, we study non-negative solutions to a nonlinear elliptic equation with a gradient term: $div(|x|^\sigma |\nabla u|^{p-2} \nabla u)=|x|^{-\tau} u^q |\nabla u|^m$ (*), where m,q>0 and 1<p\leq N. In Chapter 1, we review the literature. In Chapter 2, we completely classify the behaviour of solutions near zero for (*) where $\sigma=\tau=0$ and p=2. Suppose that 0<m<2 and m+q>1. Our classification depends on the position of q relative to a critical exponent $q_*=(N−m(N−1))/(N−2)$. We prove the following: If $q<q_*$, then any positive solution

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4

Sichau, Adrian [Verfasser]. "Robust Nonlinear Programming with Discretized PDE Constraints using Second-order Approximations / Adrian Sichau." München : Verlag Dr. Hut, 2014. http://d-nb.info/1055863125/34.

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5

Lass, Oliver [Verfasser]. "Reduced order modeling and parameter identification for coupled nonlinear PDE systems / Oliver Lass." Konstanz : Bibliothek der Universität Konstanz, 2014. http://d-nb.info/104939366X/34.

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6

Candy, Timothy Lars. "Local and global well-posedness for nonlinear Dirac type equations." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7962.

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We investigate the local and global well-posedness of a variety of nonlinear Dirac type equations with null structure on R1+1. In particular, we prove global existence in L2 for a nonlinear Dirac equation known as the Thirring model. Local existence in Hs for s > 0, and global existence for s > 1/2 , has recently been proven by Selberg-Tesfahun where they used Xs,b spaces together with a type of null form estimate. In contrast, motivated by the recent work of Machihara-Nakanishi-Tsugawa, we prove local existence in the scale invariant class L2 by using null coordinates. Moreover, again using n

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7

Vogel, Thomas. "SOLITON SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING VARIATIONAL APPROXIMATIONS AND INVERSE SCATTERING TECHNIQUES." Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3506.

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Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the er

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8

Hoang, Luan Thach. "Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/2355.

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A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associate

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9

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

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10

Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.

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11

Pooley, David. "Numerical Methods for Nonlinear Equations in Option Pricing." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1062.

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This thesis explores numerical methods for solving nonlinear partial differential equations (PDEs) that arise in option pricing problems. The goal is to develop or identify robust and efficient techniques that converge to the financially relevant solution for both one and two factor problems. To illustrate the underlying concepts, two nonlinear models are examined in detail: uncertain volatility and passport options. For any nonlinear model, implicit timestepping techniques lead to a set of discrete nonlinear equations which must be solved at each timestep. Severa

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12

Chernikov, Dmitry, and Dmitry Chernikov. "PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/626368.

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In this dissertation we investigate methods of solving various optimization problems with PDE constraints, i.e. optimization problems that have a system of partial differential equations in the set of constraints, and develop frameworks for a number of practically inspired problems that were not considered in the literature before. Such problems arise in areas like fluid mechanics, chemical engineering, finance, and other areas where a physical system needs to be optimized. In most of the literature sources on PDE-constrained optimization only relatively simple systems of PDEs are considered,

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von, Nessi Gregory Thomas, and greg vonnessi@maths anu edu au. "Regularity Results for Potential Functions of the Optimal Transportation Problem on Spheres and Related Hessian Equations." The Australian National University. Mathematical Sciences Institute, 2008. http://thesis.anu.edu.au./public/adt-ANU20081215.120059.

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In this thesis, results will be presented that pertain to the global regularity of solutions to boundary value problems having the general form \begin{align} F\left[D^2u-A(\,\cdot\,,u,Du)\right] &= B(\,\cdot\,,u,Du),\quad\text{in}\ \Omega^-,\notag\\ T_u(\Omega^-) &= \Omega^+, \end{align} where $A$, $B$, $T_u$ are all prescribed; and $\Omega^-$ along with $\Omega^+$ are bounded in $\mathbb{R}^n$, smooth and satisfying notions of c-convexity and c^*-convexity relative to one another (see [MTW05] for definitions). In particular, the case where $F$ is a quotient of symmetric functions of the eigen

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Sargent, Ethan. "Radial Solutions to Semipositone Dirichlet Problems." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/229.

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We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.

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Grupcev, Vladimir. "Symbolic Computations of Exact Solutions to Nonlinear Integrable Di®erential Equations." Scholar Commons, 2007. http://scholarcommons.usf.edu/etd/3866.

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In this thesis, first the tanh method, a method for obtaining exact traveling wave solutions to nonlinear differential equations, is introduced and described. Then the method is applied to two classes of Nonlinear Partial Differential Equations. The first one is a system of two (1 + 1)-dimensional nonlinear Korteweg-de Vries (KdV) type equations. The second one is a (3 + 1)-dimensional nonlinear wave equation. At the end, a few graphic representations of the obtained solitary wave solutions are provided, in correspondence to different values of the parameters used in the equations.

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Rossmanith, David A. Jr. "Poroacuatics Under Brinkman's Model." ScholarWorks@UNO, 2016. http://scholarworks.uno.edu/td/2183.

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Through perturbation analysis, a study of the role of Brinkman viscosity in the propagation of finite amplitude harmonic waves is carried out. Interplay between various parameters, namely, frequency, Reynolds number and beta are investigated. For systems with physically realizable Reynolds numbers, departure from the Darcy Jordan model (DJM) is noted for high frequency signals. Low and high frequency limiting cases are discussed, and the physical parameters defining the acoustic propagation are obtained. Through numerical analyses, the roles of Brinkman viscosity, the Darcy coefficient, and th

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17

Cozzi, M. "QUALITATIVE PROPERTIES OF SOLUTIONS OF NONLINEAR ANISOTROPIC PDES IN LOCAL AND NONLOCAL SETTINGS." Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/345873.

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La tesi è dedicata allo studio di varie proprietà qualitative possedute dalle soluzioni di equazioni ellittiche poste nello spazio euclideo. L'attenzione principale del lavoro è rivolta a soluzioni intere di equazioni anisotrope/eterogenee che mostrano qualche genere di proprietà di simmetria e, in particolare, che posseggono simmetria unidimensionale. L'elaborato è diviso in due parti. La prima parte è riservata ad equazioni alle derivate parziali locali, mentre la seconda si concentra su di una classe meno usuale di equazioni non locali, determinate da operatori integrali.<br>The thesis is

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18

MIRAGLIO, PIETRO. "ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/704717.

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Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dim

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19

Perrin, Charlotte. "Modèles hétérogènes en mécanique des fluides : phénomènes de congestion, écoulements granulaires et mouvement collectif." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM023/document.

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Cette thèse est dédiée à la description et à l'analyse mathématique de phénomènes d'hétérogénéités et de congestion dans les modèles de la mécanique des fluides.On montre un lien rigoureux entre des modèles de congestion douce de type Navier-Stokes compressible qui intègrent des forces de répulsion à très courte portée entre composants élémentaires; et des modèles de congestion dure de type compressible/incompressible décrivant les transitions entre zones libres et zones congestionnées.On s'intéresse ensuite à la modélisation macroscopique de mélanges formés par des particules solides immergée

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20

ALESSANDRONI, ROBERTA. "Evolution of hypersurfaces by curvature functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/661.

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Consideriamo un'ipersuperficie liscia di ℝⁿ⁺¹, con n≥2, e la sua evoluzione secondo una classe di flussi geometrici. La velocità di questi flussi ha direzione normale alla superficie e il modulo è una funzione simmetrica delle curvature principali. Inizialmente mostriamo alcune proprietà generali di questi flussi e calcoliamo l'equazione di evoluzione per una generica funzione omogenea delle curvature principali. In particolare applichiamo il flusso con velocità S=(H/(logH)), dove H è la curvatura media a meno di una costante, ad una superficie con curvatura media positiva per ottenere delle

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21

IBRAGIMOV, ANTON. "G - Expectations in infinite dimensional spaces and related PDES." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/44738.

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In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.

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22

Diedhiou, Moussa Mory. "Approche mixte interface nette-diffuse pour les problèmes d'intrusion saline en sous-sol : modélisation, analyse mathématique et illustrations numériques." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS023/document.

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Le contexte du sujet est la gestion des systèmes aquifères, en particulier le contrôle de leur exploitation et de leur éventuelle pollution. Comme exemple d'application, nous nous focalisons sur le problème d'eau salée dans les aquifères côtiers. Plus généralement, le travail s'applique à tout écoulement miscible et stratifié dans un milieu poreux faiblement déformable. Le but est d'obtenir un modèle robuste pour modéliser le déplacement des fronts de l'eau salée et de la surface supérieure de l'aquifère. Nous avons proposé une approche mixte entre interface diffuse et interface abrupte ce qui

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23

Phan, Van Long Em. "Analyse asymptotique de réseaux complexes de systèmes de réaction-diffusion." Thesis, Le Havre, 2015. http://www.theses.fr/2015LEHA0012/document.

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Le fonctionnement d'un neurone, unité fondamentale du système nerveux, intéresse de nombreuses disciplines scientifiques. Il existe ainsi des modèles mathématiques qui décrivent leur comportement par des systèmes d'EDO ou d'EDP. Plusieurs de ces modèles peuvent ensuite être couplés afin de pouvoir étudier le comportement de réseaux, systèmes complexes au sein desquels émergent des propriétés. Ce travail présente, dans un premier temps, les principaux mécanismes régissant ce fonctionnement pour en comprendre la modélisation. Plusieurs modèles sont alors présentés, jusqu'à celui de FitzHugh-Nagu

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24

Dimakos, Michail. "Linear, linearisable and integrable nonlinear PDEs." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607875.

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25

Kahler, Raphael. "On Identification of Nonlinear Parameters in PDEs." Thesis, Rochester Institute of Technology, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10117725.

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<p> Inverse problems have been studied in great detail and optimization methods using objective functionals such as output least-squares (OLS) and modified output least-squares (MOLS) are well understood. However, the existing literature has only dealt with identifying parameters that appear linearly in systems of partial differential equations. We investigate the changes that occur in the identification process if the parameter appears nonlinearly. We extend the OLS and MOLS functionals to this nonlinear case and give first and second derivative formulas. We further show that the typical conv

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26

Nendel, Max [Verfasser]. "Nonlinear expectations and a semigroup approach to fully nonlinear PDEs / Max Nendel." Konstanz : Bibliothek der Universität Konstanz, 2017. http://d-nb.info/1149510498/34.

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Forcella, Luigi. "Asymptotic problems for some classes of dispersive PDEs." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85729.

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[excerpt from the introduction]: This work deals with some classes of nonlinear dispersive evolution PDEs: in particular, under some non classical framework we will consider a class of nonlinear Schrödinger equation, a class of nonlinear Klein-Gordon equation and a system of PDEs called Zakharov system which couples a Schrödinger-type equation with a nonlinear wave equation. For all of these equations the associated Cauchy problem will be considered. More specifically we will examine two different asymptotic limits: for the Schrödinger and the Klein-Gordon equations we will deal with the

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Rossini, Eugenio. "Deep Learning and Nonlinear PDEs in High-Dimensional Spaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16859/.

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Questa tesi è incentrata sull'analisi di un algoritmo che permette di approssimare una soluzione per PDE ad alta dimensionalità. Tale algoritmo utilizza le nuove tecniche sviluppate in ambito della teoria delle Reti Neurali (Deep Learning) per affrontare un problema di difficile risoluzione. Il problema principale che affligge i modelli governati da PDE semilineari paraboliche in dimensione 100 prende il nome di "maledizione della dimensionalità". Questo non permette di utilizzare algoritmi deterministici come Galerkin o Elementi Finiti, poichè il costo computazionale cresce esponenzialmente r

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Liu, Kexue. "Nonlinear evolutionary PDEs in image processing and computer vision." College Park, Md. : University of Maryland, 2004. http://hdl.handle.net/1903/2034.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2004.<br>Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Hein, Sabine. "MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000134.

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The topic of this thesis is the theoretical and numerical research of optimal control problems for uncertain nonlinear systems, described by semilinear parabolic differential equations with additive noise, where the state is not completely available. Based on a paper by Kazufumi Ito and Karl Kunisch, which was published in 2006 with the title "Receding Horizon Control with Incomplete Observations", we analyze a Model Predictive Control (MPC) approach where the resulting linear problems on small intervals are solved with a Linear Quadratic Gaussian (LQG) design. Further we define a performance

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Papaefthymiou, Evangelos. "Systems of nonlinear PDEs arising in multilayer channel flows." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/24974.

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This thesis presents analysis and computations of systems of nonlinear partial differential equations (PDEs) modelling the dynamics of three stratified immiscible viscous layers flowing inside a channel with parallel walls inclined to the horizontal. The three layers are separated by two fluid-fluid interfaces that are free to evolve spatiotemporally and nonlinearly when the flow becomes unstable. The determination of the flow involves solution of the Navier-Stokes in domains that are changing due to the evolution of the interfaces whose position must be determined as part of the solution, pro

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Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.

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L'objectif de cette thèse est l'étude de la représentation probabiliste des différentes classes d'EDPSs non-linéaires(semi-linéaires, complètement non-linéaires, réfléchies dans un domaine) en utilisant les équations différentielles doublement stochastiques rétrogrades (EDDSRs). Cette thèse contient quatre parties différentes. Nous traitons dans la première partie les EDDSRs du second ordre (2EDDSRs). Nous montrons l'existence et l'unicité des solutions des EDDSRs en utilisant des techniques de contrôle stochastique quasi- sure. La motivation principale de cette étude est la représentation pro

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Bächtold, Michael Johannes. "Fold-type solution singularities and characteristic varieties of nonlinear PDEs /." [S.l.] : [s.n.], 2009. http://opac.nebis.ch/cgi-bin/showAbstract.pl?sys=000292630.

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Peddle, Adam. "Components of nonlinear oscillation and optimal averaging for stiff PDEs." Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/32418.

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A novel solver which uses finite wave averaging to mitigate oscillatory stiffness is proposed and analysed. We have found that triad resonances contribute to the oscillatory stiffness of the problem and that they provide a natural way of understanding stability limits and the role averaging has on reducing stiffness. In particular, an explicit formulation of the nonlinearity gives rise to a stiffness regulator function which allows for analysis of the wave averaging. A practical application of such a solver is also presented. As this method provides large timesteps at comparable computational

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Brito, Lucas Menezes de. "Métodos variacionais aplicados à problemas singulares em equações elípticas não lineares." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8860.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-06T10:34:36Z No. of bitstreams: 2 Dissertação - Lucas Menezes de Brito - 2018.pdf: 2914034 bytes, checksum: 600a20e123b6c9b15b12092b1a8071c8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-06T10:35:12Z (GMT) No. of bitstreams: 2 Dissertação - Lucas Menezes de Brito - 2018.pdf: 2914034 bytes, checksum: 600a20e123b6c9b15b12092b1a8071c8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made

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Junca, Stéphane. "Oscillating waves for nonlinear conservation laws." Habilitation à diriger des recherches, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00845827.

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The manuscript presents my research on hyperbolic Partial Differential Equations (PDE), especially on conservation laws. My works began with this thought in my mind: ''Existence and uniqueness of solutions is not the end but merely the beginning of a theory of differential equations. The really interesting questions concern the behavior of solutions.'' (P.D. Lax, The formation and decay of shock waves 1974). To study or highlight some behaviors, I started by working on geometric optics expansions (WKB) for hyperbolic PDEs. For conservation laws, existence of solutions is still a problem (for l

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Mantzavinos, Dionyssios. "Initial-boundary value problems for linear and integrable nonlinear evolution PDEs." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610568.

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Zhang, Jiwei. "Local absorbing boundary conditions for some nonlinear PDEs on unbounded domains." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1074.

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Trinh, Ngoc Tu. "Étude sur le contrôle / régulation automatique des systèmes non-linéaires hyperboliques." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1195/document.

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Dans cette étude on s'intéresse à la dynamique d'une classe de systèmes non-linéaires décrits par des équations aux dérivées partielles (EDP) du type hyperbolique. L'objectif de l'étude est de construire des lois de contrôle par feedback dynamique de la sortie afin de stabiliser le système autour d'un point d'équilibre d'une part, et, d'autre part, de réguler la sortie vers le point de consigne. Nous considérons la classe des systèmes gouvernés par des EDP quasi-linéaires du type hyperbolique à deux variables indépendantes (une variable temporelle et une variable spatiale). Pour le bien-posé d

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Lemaire, François. "Contribution à l'algorithmique en algèbre différentielle." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2002. http://tel.archives-ouvertes.fr/tel-00001363.

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Cette thèse est consacrée à l'étude des systèmes d'équations<br />différentielles non linéaires aux dérivées partielles. L'approche choisie est celle de l'algèbre différentielle. Étant donné un système d'équations différentielles, nous cherchons à obtenir des renseignements sur ses solutions. Pour ce faire, nous calculons une famille d'ensembles particuliers (appelés chaînes différentielles régulières) dont la réunion des solutions coïncide avec les solutions du système initial.<br /> <br />Les nouveaux résultats relèvent principalement du calcul formel. Le chapitre 2 clarifie le lien entre le

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Fernandes, Ray Stephen. "Very singular solutions of odd-order PDEs, with linear and nonlinear dispersion." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.507233.

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Asymptotic properties of solutions of the linear dispersion equation ut = uxxx in R × R+, and its (2k + 1)th-order generalisations are studied. General Hermitian spectral theory and asymptotic behaviour of its kernel, for the rescaled operator B = D3 + 1 3 yDy + 1 3 I, is developed, where a complete set of bi-orthonormal pair of eigenfunctions, {ψβ}, {ψ∗β }, are found. The results apply to the construction of VSS (very singular solutions) of the semilinear equation with absorption ut = uxxx − |u|p−1u in R × R+, where p > 1, which serves as a basic model for various applications, including the

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Bachouch, Achref. "Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1034/document.

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L’objectif de cette thèse est l’étude d’un schéma numérique pour l’approximation des solutions d’équations différentielles doublement stochastiques rétrogrades (EDDSR). Durant les deux dernières décennies, plusieurs méthodes ont été proposées afin de permettre la résolution numérique des équations différentielles stochastiques rétrogrades standards. Dans cette thèse, on propose une extension de l’une de ces méthodes au cas doublement stochastique. Notre méthode numérique nous permet d’attaquer une large gamme d’équations aux dérivées partielles stochastiques (EDPS) nonlinéaires. Ceci est possi

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Cirant, Marco A. "Nonlinear PDEs in ergodic control, Mean Field Games and prescribed curvature problems." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423511.

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This thesis is concerned with nonlinear elliptic PDEs and system of PDEs arising in various problems of stochastic control, differential games, specifically Mean Field Games, and differential geometry. It is divided in three parts. The first part is focused on stochastic ergodic control problems where both the state and the control space is R^d. The interest is in giving conditions on the fixed drift, the cost function and the Lagrangian function that are sufficient for synthesizing an optimal control of feedback type. In order to obtain such conditions, an approach that combines the Lyapunov

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Benatti, Luca. "Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346959.

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In the setting of Riemannian manifolds with nonnegative Ricci curvature, we provide geometric inequalities as consequences of the Monotonicity Formulas holding along the flow of the level sets of the p-capacitary potential. The work is divided into three parts. (1) In the first part, we describe the asymptotic behaviour of the p-capactitary potential in a natural class of Riemannian manifolds. (2) The second part is devoted to the proof of our Monotonicity-Rigidity Theorems. (3) In the last part, we apply the Monotonicity Theorems to obtain geometric inequalities, focusing on the Extended Mink

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Figueroa, Leonardo E. "Deterministic simulation of multi-beaded models of dilute polymer solutions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4c3414ba-415a-4109-8e98-6c4fa24f9cdc.

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We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method wit

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Trenz, Stefan [Verfasser]. "POD-Based A-posteriori Error Estimation for Control Problems Governed by Nonlinear PDEs / Stefan Trenz." Konstanz : Bibliothek der Universität Konstanz, 2017. http://d-nb.info/1142113868/34.

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GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is d

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Zhu, Hai Tao. "Investigation on EPC method for the PDF solutions of some nonlinear stochastic oscillators with poisson excitations." Thesis, University of Macau, 2009. http://umaclib3.umac.mo/record=b2120097.

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Ghilli, Daria. "Some Results in Nonlinear PDEs: Large Deviations Problems, Nonlocal Operators, and Stability for Some Isoperimetric Problems." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424479.

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This thesis is concerned with various problems arising in the study of nonlinear elliptic PDE. It is divided into three parts. In the first part we consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. Our mathematical framework is that of multiple time scale systems and singular perturbations. We are concerned with the asymptotic behaviour of a logarithmic functional of the process, which we study by methods of the theory of homogenization and singular perturbations for fully nonlinear PDEs. We point out three regim

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Ramirez, Edgardo II. "Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/28173.

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We study a parameter identification problem for the steady state diffusion equations. In this thesis, we transform this identification problem into a minimization problem by considering an appropriate cost functional and propose a finite element method for the identification of the parameter for the linear and nonlinear partial differential equation. The cost functional involves the classical output least square term, a term approximating the derivative of the piezometric head <I>u(x)</I>, an equation error term plus some regularization terms, which happen to be

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