Dynamics Of Partial Differential Equations
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Dynamics Of Partial Differential Equations
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Author : C. Eugene Wayne
language : en
Publisher: Springer
Release Date : 2015-08-08
Dynamics Of Partial Differential Equations written by C. Eugene Wayne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-08 with Mathematics categories.
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Pde Dynamics
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Author : Christian Kuehn
language : en
Publisher: SIAM
Release Date : 2019-04-10
Pde Dynamics written by Christian Kuehn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Nonlinear Dynamics In Partial Differential Equations
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Author : Shin-Ichiro Ei
language : en
Publisher:
Release Date : 2018
Nonlinear Dynamics In Partial Differential Equations written by Shin-Ichiro Ei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Effective Dynamics Of Stochastic Partial Differential Equations
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Author : Jinqiao Duan
language : en
Publisher: Elsevier
Release Date : 2014-03-06
Effective Dynamics Of Stochastic Partial Differential Equations written by Jinqiao Duan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Mathematics categories.
Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises
Partial Differential Equations And Dynamical Systems
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Author : William Edward Fitzgibbon
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1984
Partial Differential Equations And Dynamical Systems written by William Edward Fitzgibbon and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
There has recently been a great amount of activity and a rapid growth in the areas of partial differential equations and dynamical systems. This interest has been encouraged by the development of powerful new techniques in nonlinear analysis and a renewed scientific interest in applied mathematical analysis. This book has been designed to make the reader aware of progress and current problems in this exciting and useful area. The book consists of articles by internationally known mathematical scientists, based on lectures given during a year-long program at the University of Houston.
Partial Differential Equations In Fluid Dynamics
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Author : Isom H. Herron
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-28
Partial Differential Equations In Fluid Dynamics written by Isom H. Herron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-28 with Mathematics categories.
This book concerns partial differential equations applied to fluids problems in science and engineering.
Physics And Partial Differential Equations
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Author : Tatsien Li
language : en
Publisher: SIAM
Release Date : 2013-08-14
Physics And Partial Differential Equations written by Tatsien Li and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-14 with Mathematics categories.
Now available in English for the first time, Physics and Partial Differential Equations, Volume I bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.
Stochastic Pdes And Dynamics
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Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-11-21
Stochastic Pdes And Dynamics written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and Itô formula OU processes and SDEs Random attractors Applications Bibliography Index
Nonlinear Pdes A Dynamical Systems Approach
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Author : Guido Schneider
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-10-26
Nonlinear Pdes A Dynamical Systems Approach written by Guido Schneider and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-26 with Differential equations, Nonlinear categories.
This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.
Multi Dimensional Hyperbolic Partial Differential Equations
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Author : Sylvie Benzoni-Gavage
language : en
Publisher: OUP Oxford
Release Date : 2006-11-23
Multi Dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.
Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids. With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.