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Dissertations / Theses on the topic 'Differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Yantır, Ahmet Ufuktepe Ünal. "Oscillation theory for second order differential equations and dynamic equations on time scales/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000418.pdf.

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2

Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.

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3

Zheng, Ligang. "Almost periodic differential equations." Thesis, University of Ottawa (Canada), 1990. http://hdl.handle.net/10393/5766.

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In this thesis, we will study almost periodic differential equations. The motivation to study such a subject is mainly due to its wide applications. We will focus our attention on the topics of boundedness, almost periodicity, disconjugacy and the non-existence of periodic solutions for the n-body problem. Our main investigation in chapter 1 deals with Bohr almost periodic differential equations. In chapter 2, we will study Stepanov almost periodic differential equations, which is a wider class than Bohr's class and we will give a general Floquet theorem in some special cases. We devote our ef

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4

Kopfová, Jana. "Differential equations involving hysteresis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0007/NQ29055.pdf.

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5

MARINO, GISELA DORNELLES. "COMPLEX ORDINARY DIFFERENTIAL EQUATIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10175@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Neste texto estudamos diversos aspectos de singularidades de campos vetoriais holomorfos em dimensão 2. Discutimos detalhadamente o caso particular de uma singularidade sela-nó e o papel desempenhado pelas normalizações setoriais. Isto nos conduz à classificação analítica de difeomorfismos tangentes à identidade. seguir abordamos o Teorema de Seidenberg, tratando da redução de singularidades degeneradas em singularidades simples, através do procedimento de blow-up. Por fim, estudamos a demonstração do Teorema de Mattei-Moussu,

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6

Berntson, B. K. "Integrable delay-differential equations." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1566618/.

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Delay-differential equations are differential-difference equations in which the derivatives and shifts are taken with respect to the same variable. This thesis is concerned with these equations from the perspective of the theory of integrable systems, and more specifically, Painlevé equations. Both the classical Painlevé equations and their discrete analogues can be obtained as deautonomizations of equations solved by two-parameter families of elliptic functions. In analogy with this paradigm, we consider autonomous delay-differential equations solved by elliptic functions, delay-differentia

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7

Dodds, Niall. "Non-local differential equations." Thesis, University of Dundee, 2005. https://discovery.dundee.ac.uk/en/studentTheses/9eda08aa-ba49-455f-94b1-36870a1ad956.

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8

Trenn, Stephan. "Distributional differential algebraic equations." Ilmenau Univ.-Verl, 2009. http://d-nb.info/99693197X/04.

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9

Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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10

Thompson, Jeremy R. (Jeremy Ray). "Physical Motivation and Methods of Solution of Classical Partial Differential Equations." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc277898/.

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We consider three classical equations that are important examples of parabolic, elliptic, and hyperbolic partial differential equations, namely, the heat equation, the Laplace's equation, and the wave equation. We derive them from physical principles, explore methods of finding solutions, and make observations about their applications.

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11

Saravi, Masoud. "Numerical solution of linear ordinary differential equations and differential-algebraic equations by spectral methods." Thesis, Open University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446280.

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This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudospectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-sp

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12

Hollingsworth, Blane Jackson Schmidt Paul G. "Stochastic differential equations a dynamical systems approach /." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SPRING/Mathematics_and_Statistics/Dissertation/Hollingsworth_Blane_43.pdf.

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13

Luo, Hui. "Population modeling by differential equations." Huntington, WV : [Marshall University Libraries], 2007. http://www.marshall.edu/etd/descript.asp?ref=795.

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14

Allen, Brenda. "Non-smooth differential delay equations." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390472.

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15

Abourashchi, Niloufar. "Stability of stochastic differential equations." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509828.

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16

Yilmaz, Halis. "Evolution equations for differential invariants." Thesis, University of Glasgow, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274288.

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17

Piggott, Matthew David. "Geometric integration of differential equations." Thesis, University of Bath, 2002. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760826.

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18

Ranner, Thomas. "Computational surface partial differential equations." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/57647/.

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Surface partial differential equations model several natural phenomena; for example in uid mechanics, cell biology and material science. The domain of the equations can often have complex and changing morphology. This implies analytic techniques are unavailable, hence numerical methods are required. The aim of this thesis is to design and analyse three methods for solving different problems with surface partial differential equations at their core. First, we define a new finite element method for numerically approximating solutions of partial differential equations in a bulk region coupled to

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19

Tempesta, Patricia. "Simmetries in binary differential equations." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-11072017-170308/.

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The purpose of this thesis in to introduce the systematic study of symmetries in binary differential equations (BDEs). We formalize the concept of a symmetric BDE, under the linear action of a compact Lie group. One of the main results establishes a formula that relates the algebraic and geometric effects of the occurrence of the symmetry in the problem. Using tools from invariant theory and representation theory for compact Lie groups we deduce the general forms of equivariant binary differential equations under compact subgroups of O(2). A study about the behavior of the invariant straight l

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20

Fedrizzi, Ennio. "Partial differential equations and noise." Paris 7, 2012. http://www.theses.fr/2012PA077176.

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Dans ce travail, nous présentons quelques exemples des effets du bruit sur la solution d'une équation aux dérivées partielles dans trois contextes différents. Nous examinons d'abord deux équations aux dérivées partielles non linéaires dispersives, l'équation de Schrodinger non linéaire et l'équation de Korteweg - de | Vries. Nous analysons les effets d'une condition initiale aléatoire sur certaines solutions spéciales, les ! solitons. Le deuxième cas considéré est une équation aux dérive��es partielles linéaire, l'équation d'onde, avec conditions initiales aléatoires. Nous montrons qu'avec des

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21

Howard, Tamani M. "Hyperbolic Monge-Ampère Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5322/.

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In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prove some results on the Sobolev gradients that mainly arise from general nonlinear differential equatio

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22

Zhang, Wenkui. "Numerical analysis of delay differential and integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0011/NQ42489.pdf.

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23

Whitehead, Andrew John. "Differential equations and differential polynomials in the complex plane." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.273112.

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24

Zhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.

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In this thesis we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2

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25

Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switc

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26

Mohrenschildt, Martin von. "Symbolic solutions of discontinuous differential equations /." [S.l.] : [s.n.], 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10768.

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27

Fontana, Gaia. "Traffic waves and delay differential equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21211/.

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Questo elaborato si pone l'obiettivo di studiare il problema del traffico, concentrandosi su un modello semplificato in cui i veicoli sono confinati su una circonferenza e la cui velocità è determinata dal modello optimal velocity. Il discorso si sviluppa su tre capitoli: nel primo viene presentato il modello optimal velocity per il flusso del traffico e si procede a uno studio della stabilità lineare attorno al punto di equilibrio stazionario. Nel secondo capitolo lo stesso modello viene studiato nel limite termodinamico per un numero infinito di veicoli. Si ricava una soluzione costituita

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28

Gehrs, Kai Frederik. "Algorithmic methods for ordinary differential equations." [S.l.] : [s.n.], 2006. http://ubdata.uni-paderborn.de/ediss/17/2007/gehrs.

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29

Tarkhanov, Nikolai. "Unitary solutions of partial differential equations." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2985/.

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30

Ng, Chee Loong. "Parameter estimation in ordinary differential equations." Texas A&M University, 2004. http://hdl.handle.net/1969.1/388.

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The parameter estimation problem or the inverse problem of ordinary differential equations is prevalent in many process models in chemistry, molecular biology, control system design and many other engineering applications. It concerns the re-construction of auxillary parameters by fitting the solution from the system of ordinary differential equations( from a known mathematical model) to that of measured data obtained from observing the solution trajectory. Some of the traditional techniques (for example, initial value technques, multiple shooting, etc.) used to solve this class of problem ha

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31

Enstedt, Mattias. "Selected Topics in Partial Differential Equations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145763.

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This Ph.D. thesis consists of five papers and an introduction to the main topics of the thesis. In Paper I we give an abstract criteria for existence of multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. In paper II we establish existence of infinitely many solutions to the quasirelativistic Hartree-Fock equations for Coulomb systems along with properties of the solutions. In Paper III we establish existence of a ground state to the magnetic Hartree-Fock equations. In Paper IV we study the Choquard equation with general potentials (including quasirelati

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32

Taylor, S. Richard. "Probabilistic Properties of Delay Differential Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1183.

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Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable.

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33

Head, Gerald. "Uniqueness of Solutions of Differential Equations." TopSCHOLAR®, 1995. http://digitalcommons.wku.edu/theses/913.

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Uniqueness of solutions for ordinary differential equations is studied. The classical theorems which guarantee uniqueness are surveyed, including discussion and examples. Other results concerning uniqueness are considered in the final chapter, including the relationship between convergence of successive approximations and uniqueness, non-uniqueness and continuous dependence on initial conditions.

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34

Rassias, Stamatiki. "Stochastic functional differential equations and applications." Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486536.

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The general truth that the principle of causality, that is, the future state of a system is independent of its past history, cannot support all the cases under consideration, leads to the introduction of the FDEs. However, the strong need of modelling real life problems, demands the inclusion of stochasticity. Thus, the appearance of the SFDEs (special case of which is the SDDEs) is necessary and definitely unavoidable. It has been almost a century since Langevin's model that the researchers incorporate noise terms into their work. Two of the main research interests are linked with the existen

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35

Guo, Yujin. "Partial differential equations of electrostatic MEMS." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31315.

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Micro-Electromechanical Systems (MEMS) combine electronics with micro-size mechanical devices in the process of designing various types of microscopic machinery, especially those involved in conceiving and building modern sensors. Since their initial development in the 1980s, MEMS has revolutionized numerous branches of science and industry. Indeed, MEMS-based devices are now essential components of modern designs in a variety of areas, such as in commercial systems, the biomedical industry, space exploration, telecommunications, and other fields of applications. As it is often the case in sci

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36

Keane, Therese Alison Mathematics &amp Statistics Faculty of Science UNSW. "Combat modelling with partial differential equations." Awarded By:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43086.

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In Part I of this thesis we extend the Lanchester Ordinary Differential Equations and construct a new physically meaningful set of partial differential equations with the aim of more realistically representing soldier dynamics in order to enable a deeper understanding of the nature of conflict. Spatial force movement and troop interaction components are represented with both local and non-local terms, using techniques developed in biological aggregation modelling. A highly accurate flux limiter numerical method ensuring positivity and mass conservation is used, addressing the difficulties of i

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37

Arslan, Sevgi. "Nonlinear Differential Equations with Biological Applications." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-28410.

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38

Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.

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The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow;

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39

Ron, Eyal [Verfasser]. "Hysteresis-Delay Differential Equations / Eyal Ron." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1121588026/34.

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40

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s

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41

Seiß, Matthias [Verfasser]. "Root parametrized differential equations / Matthias Seiß." Kassel : Universitätsbibliothek Kassel, 2012. http://d-nb.info/1028081170/34.

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42

Williams, David Robert Emlyn. "Differential equations driven by discontiuous paths." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300842.

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43

Stoleriu, Iulian. "Integro-differential equations in materials science." Thesis, University of Strathclyde, 2001. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=21413.

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This thesis deals with nonlocal models for solid-solid phase transitions, such as ferromagnetic phase transition or phase separation in binary alloys. We discuss here, among others, nonlocal versions of the Allen-Cahn and Cahn-Hilliard equations, as well as a nonlocal version of the viscous Cahn-Hilliard equation. The analysis of these models can be motivated by the fact that their local analogues fail to be applicable when the wavelength of microstructure is very small, e. g. at the nanometre scale. Though the solutions of these nonlocal equations and those of the local versions share some co

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44

Wu, Chengfa, and 吳成發. "Meromorphic solutions of complex differential equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/206466.

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The objective of this thesis is to study meromorphic solutions of complex algebraic ordinary differential equations (ODEs). The thesis consists of two main themes. One of them is to find explicitly all meromorphic solutions of certain class of complex algebraic ODEs. Since constructing explicit solutions of complex ODEs in general is very difficult, the other theme (motivated by the classical conjecture proposed by Hayman in 1996) is to establish estimations on the growth of meromorphic solutions in terms of Nevanlinna characteristic function. The tools from complex analysis that will be us

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45

Adamopoulou, Panagiota-Maria. "Differential equations and quantum integrable systems." Thesis, University of Kent, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.655223.

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This thesis explores several aspects of the correspondence between classes of linear ordinary differential equations (ODEs) in the complex plane and certain quantum integrable models (IMs), also known as the ODE/IM correspondence. First, we enlarge the set of ordinary differential equations that enter the correspondence. Differential equations satisfied by Wronskians between solutions of specific ODEs are obtained and are associated to nodes of particular Dynkin diagrams. In the second part of the thesis we generalise the correspondence to encompass massive IMs. Starting from an integrable non

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46

Kirby, P. J. "The theory of exponential differential equations." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433471.

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This thesis is a model-theoretic study of exponential differential equations in the context of differential algebra. I define the theory of a set of differential equations and give an axiomatization for the theory of the exponential differential equations of split semiabelian varieties. In particular, this includes the theory of the equations satisfied by the usual complex exponential function and the Weierstrass p-functions. The theory consists of a description of the algebraic structure on the solution sets together with necessary and sufficient conditions for a system of equations to have s

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47

Lloyd, David J. B. "Localised solutions of partial differential equations." Thesis, University of Bristol, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434765.

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48

Zhu, Wei. "Fractional differential equations in risk theory." Thesis, University of Liverpool, 2018. http://livrepository.liverpool.ac.uk/3018514/.

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This thesis considers one of the central topics in the actuarial mathematics literature, deriving the probability of ruin in the collective risk model. The classical risk model and renewal risk models are focused in this project, where the claim number processes are assumed to be Poisson counting processes and any general renewal counting processes, respectively. The first part of this project is about the classical risk model. We look at the case when claim sizes follow a gamma distribution. Explicit expressions for ruin probabilities are derived via Laplace transform and inverse Laplace tran

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49

Lin, Kevin K. (Kevin Kwei-yu) 1974. "Coordinate-independent computations on differential equations." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42798.

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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.<br>Includes bibliographical references (v. 2, p. 512-514).<br>by Kevin K. Lin.<br>M.Eng.

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50

Désilles, Gaël 1971. "Differential Kolmogorov equations for transiting processes." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/49643.

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