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• The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

Numerics of Elastic and Acoustic Wave Motion

Virta, Kristoffer January 2016 (has links)
The elastic wave equation describes the propagation of elastic disturbances produced by seismic events in the Earth or vibrations in plates and beams. The acoustic wave equation governs the propagation of sound. The description of the wave fields resulting from an initial configuration or time dependent forces is a valuable tool when gaining insight into the effects of the layering of the Earth, the propagation of earthquakes or the behavior of underwater sound. In the most general case exact solutions to both the elastic wave equation and the acoustic wave equation are impossible to construct. Numerical methods that produce approximative solutions to the underlaying equations now become valuable tools. In this thesis we construct numerical solvers for the elastic and acoustic wave equations with focus on stability, high order of accuracy, boundary conditions and geometric flexibility. The numerical solvers are used to study wave boundary interactions and effects of curved geometries. We also compare the methods that we have constructed to other methods for the simulation of elastic and acoustic wave motion.
32

Existence of a Solution for a Wave Equation and an Elliptic Dirichlet Problem

Sumalee Unsurangsie 05 1900 (has links)
In this paper we consider an existence of a solution for a nonlinear nonmonotone wave equation in [0,π]xR and an existence of a positive solution for a non-positone Dirichlet problem in a bounded subset of R^n.
33

An analysis of the symmetries and conservation laws of some classes of nonlinear wave equations in curved spacetime geometry

Jamal, S 08 August 2013 (has links)
A thesis submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Doctor of Philosophy, Johannesburg, 2013. / The (1+3) dimensional wave and Klein-Gordon equations are constructed using the covariant d'Alembertian operator on several spacetimes of interest. Equations on curved geometry inherit the nonlinearities of the geometry. These equations display interesting properties in a number of ways. In particular, the number of symmetries and therefore, the conservation laws reduce depending on how curved the manifold is. We study the symmetry properties and conservation laws of wave equations on Freidmann-Robertson-Walker, Milne, Bianchi, and de Sitter universes. Symmetry structures are used to reduce the number of unknown functions, and hence contribute to nding exact solutions of the equations. As expected, properties of reduction procedures using symmetries, variational structures and conservation laws are more involved than on the well known at (Minkowski) manifold.
34

Atratores para equações de ondas em domínios de fronteira móvel / Attractors for a weakly damped semilinear wave equation on time-varying domains

Chuño, Christian Manuel Surco 09 June 2014 (has links)
Este trabalho contém um estudo sobre equações de ondas fracamente dissipativas definidas em domínios de fronteira móvel &part;2u/&part;t2/ + &eta;&part;u/&part;t - &Delta;u + g(u) = f(x,t), (x,t) &isin; ^D&tau;, onde ^D&tau; = &CUP;t&isin;(&tau;,+ &infin;) Ot X . Dizemos que domínio D&tau; possui fronteira móvel se admitirmos que a fronteira &Gamma;t de de Ot varia em relação a t. Nossa contribuição é dividida em três etapas. 1 - Provamos que o problema munido da condição de fronteira de Dirichlet é bem posto no sentido de Hadamard (existência global, unicidade e dependência contínua dos dados) para soluções fortes e fracas. Nessa etapa utilizamos um método clássico que transforma o domínio dependente de t em um domínio fixo. Como consequência observamos que o sistema é essencialmente não autônomo. 2 - Buscamos uma teoria de sistemas dinâmicos não autônomos para estudar o operador solução do problema como um processo U(t; &tau;) : X&tau; &rarr; X&tau;, t&ge; &tau;, definido em espaços de fase Xt = H01(Ot) &#215; L2(Ot) que são dependentes do tempo t. 3 - No contexto da dinâmica de longo prazo encontramos hipóteses para garantir que o sistema dinâmico associado ao problema de ondas em domínios de fronteira móvel possui um atrator pullback. Basicamente admitimos que o domínio é crescente e \"time-like\". Salientamos que o nosso trabalho é o primeiro que estuda tais equações de ondas sob o ponto de vista de sistemas dinâmicos não-autônomos. Para equações parabólicas, resultados no mesmo contexto foram obtidos anteriormente por Kloeden, Marín-Rubio e Real [JDE 244 (2008) 2062-2090] e Kloeden, Real e Sun [JDE 246 (2009) 4702-4730]. Entretanto o nosso problema á hiperbólico e nã possui a regularidade das equações parabólicas. / In this work we study a weakly dissipative wave equation defined in domains with moving boundary &part;2u/&part;t2/ + &eta;&part;u/&part;t - &Delta;u + g(u) = f(x,t), (x,t) &isin; D&tau;, where D&tau> = &CUP;t&isin;(&tau;,+ &infin;) Ot X . We says that a domain D&tau has moving boundary if the boundary &Gama;t of Ot varies with respect to t. Our contribution is threefold. 1 - We prove that the wave equation equipped with Dirichlet boundary condition is well-posed in the sense of Hadamard (global existence, uniqueness and continuous dependence with respect to data) for weak and strong solutions. This is done by using a classical argument that transforms the time dependent domain in a fixed domain. As a consequence we see that the problem is essentially non-autonomous. 2 -We find a theory of non-autonomous dynamical systems in order to study the solution operator as a process U(t; &tau;) : X&tau; &rarr; Xsub>t, t&ge;&tau;, defined in time dependent phase spaces Xt = H01 (Ot) &#215; L2.(Ot. 3 - In the context of long-time behavior of solutions we find suitable conditions to guarantee the existence of a pullback attractor. Roughly speaking, we assume the domain Q is expanding and time-like. We emphasize that our work is the first one that consider wave equations in noncylindrical domains as non-autonomous dynamical systems. With respect to parabolic equations, similar results were early obtained by Kloeden, Marín-Rubio and Real [JDE 244 (2008) 2062-2090] and Kloeden, Real and Sun [JDE 246 (2009) 4702-4730]. However our problem is hyperbolic and does not enjoy regularity properties as the parabolic ones.
35

The Nonisospectral and variable coefficient Korteweg-de Vries equation.

January 1992 (has links)
by Li Kam Shun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaf 65). / Chapter CHAPTER 1 --- Soliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §1.1 --- Introduction --- p.4 / Chapter §1.2 --- Inverse Scattering --- p.6 / Chapter §1.3 --- N-Soliton Solution --- p.11 / Chapter §1.4 --- One-Soliton Solutions --- p.15 / Chapter §1.5 --- Two-Soliton Solutions --- p.18 / Chapter §1.6 --- Oscillating and Asymptotically Standing Solitons --- p.23 / Chapter CHAPTER 2 --- Asymptotic Behaviour of Nonsoliton Solutions of the Nonisospectral and Variable Coefficient Korteweg-de Vries Equation / Chapter §2.1 --- Introduction --- p.31 / Chapter §2.2 --- Main Results --- p.36 / Chapter §2.3 --- Lemmas --- p.39 / Chapter §2.4 --- Proof of the Main Results --- p.59 / References --- p.65
36

Properties of quasinormal modes in open systems.

January 1995 (has links)
by Tong Shiu Sing Dominic. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 236-241). / Acknowledgements --- p.iv / Abstract --- p.v / Chapter 1 --- Open Systems and Quasinormal Modes --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Non-Hermitian Systems --- p.1 / Chapter 1.1.2 --- Optical Cavities as Open Systems --- p.3 / Chapter 1.1.3 --- Outline of this Thesis --- p.6 / Chapter 1.2 --- Simple Models of Open Systems --- p.10 / Chapter 1.3 --- Contributions of the Author --- p.14 / Chapter 2 --- Completeness and Orthogonality --- p.16 / Chapter 2.1 --- Introduction --- p.16 / Chapter 2.2 --- Green's Function of the Open System --- p.19 / Chapter 2.3 --- High Frequency Behaviour of the Green's Function --- p.24 / Chapter 2.4 --- Completeness of Quasinormal Modes --- p.29 / Chapter 2. 5 --- Method of Projection --- p.31 / Chapter 2.5.1 --- Problems with the Usual Method of Projection --- p.31 / Chapter 2.5.2 --- Modified Method of Projection --- p.33 / Chapter 2.6 --- Uniqueness of Representation --- p.38 / Chapter 2.7 --- Definition of Inner Product and Quasi-Stationary States --- p.39 / Chapter 2.7.1 --- Orthogonal Relation of Quasinormal Modes --- p.39 / Chapter 2.7.2 --- Definition of Hilbert Space and State Vectors --- p.41 / Chapter 2.8 --- Hermitian Limits --- p.43 / Chapter 2.9 --- Numerical Examples --- p.45 / Chapter 3 --- Time-Independent Perturbation --- p.58 / Chapter 3.1 --- Introduction --- p.58 / Chapter 3.2 --- Formalism --- p.60 / Chapter 3.2.1 --- Expansion of the Perturbed Quasi-Stationary States --- p.60 / Chapter 3.2.2 --- Formal Solution --- p.62 / Chapter 3.2.3 --- Perturbative Series --- p.66 / Chapter 3.3 --- Diagrammatic Perturbation --- p.70 / Chapter 3.3.1 --- Series Representation of the Green's Function --- p.70 / Chapter 3.3.2 --- Eigenfrequencies --- p.73 / Chapter 3.3.3 --- Eigenfunctions --- p.75 / Chapter 3.4 --- Numerical Examples --- p.77 / Chapter 4 --- Method of Diagonization --- p.81 / Chapter 4.1 --- Introduction --- p.81 / Chapter 4.2 --- Formalism --- p.82 / Chapter 4.2.1 --- Matrix Equation with Non-unique Solution --- p.82 / Chapter 4.2.2 --- Matrix Equation with a Unique Solution --- p.88 / Chapter 4.3 --- Numerical Examples --- p.91 / Chapter 5 --- Evolution of the Open System --- p.97 / Chapter 5.1 --- Introduction --- p.97 / Chapter 5.2 --- Evolution with Arbitrary Initial Conditions --- p.99 / Chapter 5.3 --- Evolution with the Outgoing Plane Wave Condition --- p.106 / Chapter 5.3.1 --- Evolution Inside the Cavity --- p.106 / Chapter 5.3.2 --- Evolution Outside the Cavity --- p.110 / Chapter 5.4 --- Physical Implications --- p.112 / Chapter 6 --- Time-Dependent Perturbation --- p.114 / Chapter 6.1 --- Introduction --- p.114 / Chapter 6.2 --- Inhomogeneous Wave Equation --- p.117 / Chapter 6.3 --- Perturbative Scheme --- p.120 / Chapter 6.4 --- Energy Changes due to the Perturbation --- p.128 / Chapter 6.5 --- Numerical Examples --- p.131 / Chapter 7 --- Adiabatic Approximation --- p.150 / Chapter 7.1 --- Introduction --- p.150 / Chapter 7.2 --- The Effect of a Varying Refractive Index --- p.153 / Chapter 7.3 --- Adiabatic Expansion --- p.156 / Chapter 7.4 --- Numerical Examples --- p.167 / Chapter 8 --- Generalization of the Formalism --- p.176 / Chapter 8. 1 --- Introduction --- p.176 / Chapter 8.2 --- Generalization of the Orthogonal Relation --- p.180 / Chapter 8.3 --- Evolution with the Outgong Wave Condition --- p.183 / Chapter 8.4 --- Uniform Convergence of the Series Representation --- p.193 / Chapter 8.5 --- Uniqueness of Representation --- p.200 / Chapter 8.6 --- Generalization of Standard Calculations --- p.202 / Chapter 8.6.1 --- Time-Independent Perturbation --- p.203 / Chapter 8.6.2 --- Method of Diagonization --- p.206 / Chapter 8.6.3 --- Remarks on Dynamical Calculations --- p.208 / Appendix A --- p.209 / Appendix B --- p.213 / Appendix C --- p.225 / Appendix D --- p.231 / Appendix E --- p.234 / References --- p.236
37

Waves in a cavity with an oscillating boundary =: 振動空腔中的波動. / 振動空腔中的波動 / Waves in a cavity with an oscillating boundary =: Zhen dong kong qiang zhong de bo dong. / Zhen dong kong qiang zhong de bo dong

January 1999 (has links)
by Ho Yum Bun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 93-94). / Text in English; abstracts in English and Chinese. / by Ho Yum Bun. / List of Figures --- p.3 / Abstract --- p.9 / Chinese Abstract --- p.10 / Acknowledgement --- p.11 / Chapter 1 --- Introduction --- p.12 / Chapter 1.1 --- Motivation --- p.12 / Chapter 1.2 --- What is Sonoluminescence? --- p.13 / Chapter 1.3 --- The Main Task of this Project --- p.13 / Chapter 1.4 --- Organization of this Thesis --- p.13 / Chapter 2 --- Reviews on One-dimensional Dynamical Cavity Problem --- p.15 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Formulation --- p.15 / Chapter 2.3 --- Moore's R Function Method --- p.18 / Chapter 2.4 --- Mode Expansion Method --- p.19 / Chapter 2.5 --- Transformation method --- p.20 / Chapter 2-6 --- Summary --- p.21 / Chapter 3 --- Numerical Results For One-dimensional Dynamical Cavity Prob- lem --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Evolution of a Cavity System --- p.23 / Chapter 3.3 --- Motion of the Moving Mirror --- p.23 / Chapter 3.4 --- R(z) Function --- p.24 / Chapter 3.4.1 --- Construction of R(z) Function --- p.24 / Chapter 3.4.2 --- Numerical R(z) Function --- p.27 / Chapter 3.5 --- Results --- p.27 / Chapter 3.5.1 --- Results with Moore's R(z) Function Method --- p.27 / Chapter 3.5.2 --- Results with the Mode Expansion Method --- p.29 / Chapter 3.5.3 --- Results with the Transformation Method --- p.36 / Chapter 3.6 --- Summary --- p.36 / Chapter 4 --- Spherical Dynamical Cavity Problem --- p.37 / Chapter 4.1 --- Introduction --- p.37 / Chapter 4.2 --- Formulation --- p.37 / Chapter 4.3 --- Motion of a Moving Spherical Mirror --- p.39 / Chapter 4.4 --- Summary --- p.40 / Chapter 5 --- The G(z) Function Method --- p.41 / Chapter 5.1 --- Introduction --- p.41 / Chapter 5.2 --- G(z) Function --- p.42 / Chapter 5.2.1 --- Ideas of Deriving the G(z) Function --- p.42 / Chapter 5.2.2 --- Formalism --- p.42 / Chapter 5.2.3 --- Initial G(z) Function --- p.45 / Chapter 5.3 --- Construction of the G(z) Function --- p.46 / Chapter 5.3.1 --- Case I : l=0 --- p.46 / Chapter 5.3.2 --- Case II : l > 0 --- p.49 / Chapter 5.4 --- Asymptotic Series Solution of G(z) --- p.50 / Chapter 5.5 --- Application to Resonant Mirror Motion --- p.52 / Chapter 5.6 --- Regularization of G(z) --- p.58 / Chapter 5.7 --- Behaviors of the Fields --- p.58 / Chapter 5.7.1 --- z vs tf Graph --- p.61 / Chapter 5.7.2 --- Case 1: l= 0 --- p.61 / Chapter 5.7.3 --- "Case2: l= 1,2" --- p.62 / Chapter 5.7.4 --- Case 3: l= 3 --- p.73 / Chapter 5.7.5 --- Section Summary --- p.73 / Chapter 5.8 --- Summary --- p.73 / Chapter 6 --- Three-dimensional Mode Expansion Method and Transforma- tion Method --- p.75 / Chapter 6.1 --- Introduction --- p.75 / Chapter 6.2 --- Mode Expansion Method --- p.75 / Chapter 6.2.1 --- Formalism --- p.75 / Chapter 6.2.2 --- Application of Floquet's Theory --- p.78 / Chapter 6.2.3 --- Results --- p.80 / Chapter 6.3 --- The Transformation Method --- p.80 / Chapter 6.3.1 --- The Method --- p.80 / Chapter 6.3.2 --- Numerical Schemes --- p.86 / Chapter 6.3.3 --- Results --- p.89 / Chapter 6.4 --- Summary --- p.89 / Chapter 7 --- Conclusion --- p.90 / Chapter 7.1 --- The One-dimensional Dynamical Cavity Problem --- p.90 / Chapter 7.2 --- The Dynamical Spherical Cavity Problem --- p.91 / Chapter 7.3 --- Numerical Methods --- p.91 / Chapter 7.4 --- Further Investigation --- p.92 / Bibliography --- p.93
38

A survey on linearized method for inverse wave equations.

January 2012 (has links)

39

On a shallow water equation.

January 2001 (has links)
Zhou Yong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 51-53). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.2 / Chapter 2 --- Preliminaries --- p.10 / Chapter 3 --- Periodic Case --- p.22 / Chapter 4 --- Non-periodic Case --- p.35 / Bibliography --- p.51
40

Approximations hyperboliques des équations de Navier-Stokes / Hyperbolic approximations of the Navier-Stokes equations

Hachicha, Imène 15 November 2013 (has links)
Dans cette thèse, nous nous intéressons à deux approximations hyperboliques des équations de Navier-Stokes incompressibles en dimensions 2 et 3 d'espace. Dans un premier temps, on considère une perturbation hyperbolique de l'équation de la chaleur, introduite par Cattaneo en 1949, pour remédier au paradoxe de la propagation instantanée de cette équation. En 2004, Brenier, Natalini et Puel remarquent que la même perturbation, qui consiste à rajouter ε∂tt à l'équation, intervient en relaxant les équations d'Euler. En dimension 2, les auteurs montrent que, pour des sonnées régulières et sous certaines hypothèses de petitesse, la solution globale de la perturbation converge vers l'unique solution globale de (NS). En 2007, Paicu et Raugel améliorent les résultats de [BNP] en étendant la théorie à la dimension 3 et en prenant des données beaucoup moins régulières. Nous avons obtenu des résultats de convergence, avec données de régularité quasi-critique, qui complètent et prolongent ceux de [BNP] et [PR]. La seconde approximation que l'on considère est un nouveau modèle hyperbolique à vitesse de propagation finie. Ce modèle est obtenu en pénalisant la contrainte d'incompressibilité dans la perturbation de Cattaneo. Nous démontrons que les résultats d'existence globale et de convergence du précédent modèle sont encore vérifiés pour celui-ci. / In this work, we are interested in two hyperbolic approximations of the 2D and 3D Navier-Stokes equations. The first model we consider comes from Cattaneo's hyperbolic perturbation of the heat equation to obtain a finite speed of propagation equation. Brenier, Natalini and Puel studied the same perturbation as a relaxed version of the 2D Euler equations and proved that the solution to this relaxation converges towards the solution to (NS) with smooth data, provided some smallness assumptions. Later, Paicu and Raugel improved their results, extending the theory to the 3D setting and requiring significantly less regular data. Following [BNP] and [PR], we prove global existence and convergence results with quasi-critical regularity assumptions on the initial data. In the second part, we introduce a new hyperbolic model with finite speed of propagation, obtained by penalizing the incompressibility constraint in Cattaneo's perturbation. We prove that the same global existence and convergence results hold for this model as well as for the first one.

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