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Dissertations / Theses on the topic 'System of nonlinear differential equations'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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2

Zerihun, Tadesse G. "Nonlinear Techniques for Stochastic Systems of Differential Equations." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4970.

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Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematical

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3

Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.

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This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 E

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4

SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.

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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variationa

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5

Leiva, Hugo. "Skew-product semiflows and time-dependent dynamical systems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/29912.

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6

馮漢國 and Hon-kwok Fung. "Some linear preserver problems in system theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B3121227X.

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7

Fung, Hon-kwok. "Some linear preserver problems in system theory /." [Hong Kong] : University of Hong Kong, 1995. http://sunzi.lib.hku.hk/hkuto/record.jsp?B16121673.

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8

Di, Cosmo Jonathan. "Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209863.

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The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a mathematical point of view, the study of this equation is interesting and delicate, notably because it can have a very rich set of solutions with various behaviours.<p><p>In this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outsid

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9

Van, der Walt Jan Harm. "Generalized solutions of systems of nonlinear partial differential equations." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-05242009-122628.

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10

Wu, Xiaoming. "Partial differential equations with applications to wave propagation." Thesis, University of Newcastle Upon Tyne, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239573.

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11

Handel, Andreas. "Limits of Localized Control in Extended Nonlinear Systems." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5025.

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We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance

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12

Rejoub, Riad A. "Projective and non-projective systems of first order nonlinear differential equations." Scholarly Commons, 1992. https://scholarlycommons.pacific.edu/uop_etds/2228.

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It is well established that many physical and chemical phenomena such as those in chemical reaction kinetics, laser cavities, rotating fluids, and in plasmas and in solid state physics are governed by nonlinear differential equations whose solutions are of variable character and even may lack regularities. Such systems are usually first studied qualitatively by examining their temporal behavior near singular points of their phase portrait. In this work we will be concerned with systems governed by the time evolution equations [see PDF for mathematical formulas] The xi may generally be consider

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13

Yang, Lixiang. "Modeling Waves in Linear and Nonlinear Solids by First-Order Hyperbolic Differential Equations." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1303846979.

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14

See, Chong Wee Simon. "Numerical methods for the simulation of dynamic discontinuous systems." Thesis, University of Salford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358276.

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15

Ahlip, Rehez Ajmal. "Stability & filtering of stochastic systems." Thesis, Queensland University of Technology, 1997.

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16

Philipowski, Robert. "Stochastic interacting particle systems and nonlinear partial differential equations from fluid mechanics." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=986005622.

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17

Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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18

Ali, Jaffar. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Diss., Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-07082008-153843.

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19

Smario, David J. "Multicorrelation analysis and state space reconstruction /." Online version of thesis, 1994. http://hdl.handle.net/1850/11443.

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20

Chan, Chuen Lit. "A perturbation-incremental (PI) method for strongly non-linear oscillators and systems of delay differential equations /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b1988767xa.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2005.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 121-133)

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21

Marahrens, Daniel. "On some nonlinear partial differential equations for classical and quantum many body systems." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/244203.

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This thesis deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that in the hydrodynamic limit, the particle densities of a one-dimensional zero range process on a periodic lattice converge to the solution of a nonlinear diffusion equation. This method allows for the first time an explicit uniform-in-time bound on the rate of convergence in the hydrodynamic lim

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22

Gerdin, Markus. "Identification and Estimation for Models Described by Differential-Algebraic Equations." Doctoral thesis, Linköping : Department of Electrical Engineering, Linköpings universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7600.

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23

Mulvey, Joseph Anthony. "Symmetry methods for integrable systems." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5379/.

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This thesis discusses various properties of a number of differential equations which we will term "integrable". There are many definitions of this word, but we will confine ourselves to two possible characterisations — either an equation can be transformed by a suitable change of variables to a linear equation, or there exists an infinite number of conserved quantities associated with the equation that commute with each other via some Hamiltonian structure. Both of these definitions rely heavily on the concept of the symmetry of a differential equation, and so Chapters 1 and 2 introduce and ex

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24

Steinhauer, Mark. "On analysis of some nonlinear systems of partial differential equations of continuum mechanics." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/54890745.html.

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25

Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.

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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformat

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26

Bobade, Parag Suhas. "Modeling, Approximation, and Control for a Class of Nonlinear Systems." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/80978.

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This work investigates modeling, approximation, estimation, and control for classes of nonlinear systems whose state evolves in space $mathbb{R}^n times H$, where $mathbb{R}^n$ is a n-dimensional Euclidean space and $H$ is a infinite dimensional Hilbert space. Specifically, two classes of nonlinear systems are studied in this dissertation. The first topic develops a novel framework for adaptive estimation of nonlinear systems using reproducing kernel Hilbert spaces. A nonlinear adaptive estimation problem is cast as a time-varying estimation problem in $mathbb{R}^d times H$. In contrast to mo

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27

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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28

Au, Kin Chung. "Differential techniques for scalable and interactive mesh editing /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?CSED%202007%20AU.

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29

Zhang, Xiaohong. "Optimal feedback control for nonlinear discrete systems and applications to optimal control of nonlinear periodic ordinary differential equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40185.

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30

Pereira, da Silva João Gustavo [Verfasser]. "Modelling Flash Sintering Using Systems of Nonlinear Differential Equations / João Gustavo Pereira da Silva." München : Verlag Dr. Hut, 2019. http://d-nb.info/1190421836/34.

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31

Ye, Jinglong. "Infinite semipositone systems." Diss., Mississippi State : Mississippi State University, 2009. http://library.msstate.edu/etd/show.asp?etd=etd-07072009-132254.

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32

Leto, Jonathan. "SOLITARY WAVE FAMILIES IN TWO NON-INTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY." Master's thesis, University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3504.

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In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturban

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33

Smith, Todd Blanton. "Variational embedded solitons, and traveling wavetrains generated by generalized Hopf bifurcations, in some NLPDE systems." Doctoral diss., University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5042.

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In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary w

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34

Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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35

Gilmour, Isla. "Nonlinear model evaluation : ɩ-shadowing, probabilistic prediction and weather forecasting". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298797.

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Physical processes are often modelled using nonlinear dynamical systems. If such models are relevant then they should be capable of demonstrating behaviour observed in the physical process. In this thesis a new measure of model optimality is introduced: the distribution of ɩ-shadowing times defines the durations over which there exists a model trajectory consistent with the observations. By recognising the uncertainty present in every observation, including the initial condition, ɩ-shadowing distinguishes model sensitivity from model error; a perfect model will always be accepted as optimal. T

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36

Schlöder, Johannes P. "Numerische Methoden zur Behandlung hochdimensionaler Aufgaben der Parameteridentifizierung." Bonn : [s.n.], 1987. http://catalog.hathitrust.org/api/volumes/oclc/18814825.html.

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37

Bradley, Aoibhinn Maire. "Analysis of nonlinear spatio-temporal partial differential equations : applications to host-parasite systems and bubble growth." Thesis, University of Strathclyde, 2014. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=24405.

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The mountain hare population currently appears to be under threat in Scotland. The natural population cycles exhibited by this species are thought to be, at least in part, due to its infestation by a parasitic worm. We seek to gain an understanding of these population dynamics through a mathematical model of this system and so determine whether low population levels observed in the field are a natural trough associated with this cycling, or whether they point to a more serious decline in overall population densities. A generic result, that can be used to predict the presence of periodic travel

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38

Graham, David(David Warwick) 1976. "Forced Brakke flows." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/7774.

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39

Graham, David (David Warwick) 1976. "Forced Brakke flows." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/5712.

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40

Clinger, Richard A. "Stability Analysis of Systems of Difference Equations." VCU Scholars Compass, 2007. http://hdl.handle.net/10156/1318.

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41

Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.

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Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamic

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42

Felts, K. R. Chicone Carmen Charles. "Oscillators resonances and excitations /." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6147.

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Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Carmen Chicone Vita. Includes bibliographical references.

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43

Kalamangalam, G. P. "Nonlinear oscillations and chaos in chemical cardiorespiratory control." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296830.

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We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate n

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44

Lindgren, Joseph B. "Orbital Stability Results for Soliton Solutions to Nonlinear Schrödinger Equations with External Potentials." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/46.

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For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method. For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

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45

Ferrara, Joseph. "A Study of Nonlinear Dynamics in Mathematical Biology." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/448.

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We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

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46

Matthes, Michael [Verfasser], Caren [Akademischer Betreuer] Tischendorf, and Tassilo [Akademischer Betreuer] Küpper. "Numerical Analysis of Nonlinear Partial Differential-Algebraic Equations: A Coupled and an Abstract Systems Approach / Michael Matthes. Gutachter: Caren Tischendorf ; Tassilo Küpper." Köln : Universitäts- und Stadtbibliothek Köln, 2012. http://d-nb.info/1038359600/34.

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47

Druet, Pierre-Etienne. "Analysis of a coupled system of partial differential equations modeling the interaction between melt flow, global heat transfer and applied magnetic fields in crystal growth." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2009. http://dx.doi.org/10.18452/15893.

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Hauptthema der Dissertation ist die Analysis eines nichtlinearen, gekoppelten Systems partieller Differentialgleichungen (PDG), das in der Modellierung der Kristallzüchtung aus der Schmelze mit Magnetfeldern vorkommt. Die zu beschreibenden Phenomäne sind einerseits der im elektromagnetisch geheizten Schmelzofen erfolgende Wärmetransport (Wärmeleitung, -konvektion und -strahlung), und andererseits die Bewegung der Halbleiterschmelze unter dem Einfluss der thermischen Konvektion und der angewendeten elektromagnetischen Kräfte. Das Modell besteht aus den Navier-Stokeschen Gleichungen für eine

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48

Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.

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49

Pittayakanchit, Weerapat. "The Global Stability of the Solution to the Morse Potential in a Catastrophic Regime." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/72.

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Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any s

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50

Swatzel, James Paul. "A partial differential equation to model the Tacoma Narrows Bridge failure." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2631.

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The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.

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