Dynamics Of Partial Differential Equations

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Methods For Constructing Exact Solutions Of Partial Differential Equations
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Author : Sergey V. Meleshko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18
Methods For Constructing Exact Solutions Of Partial Differential Equations written by Sergey V. Meleshko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-18 with Technology & Engineering categories.
Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Applied Partial Differential Equations
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Author : Peter Markowich
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06
Applied Partial Differential Equations written by Peter Markowich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-06 with Mathematics categories.
This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.
Nonlinear Dynamics In Partial Differential Equations
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Author : Shin'ichirō Ei
language : en
Publisher: Mathematical Society of Japan, Japan
Release Date : 2015
Nonlinear Dynamics In Partial Differential Equations written by Shin'ichirō Ei and has been published by Mathematical Society of Japan, Japan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This volume contains more than fifty peer-reviewed survey and research papers presented at the 4th MSJ-SI International Conference on Nonlinear Dynamics in Partial Differential Equations, held at Kyushu University, Kyushu, Japan, September 12-21, 2011. Nonlinear partial differential equations describing nonlinear dynamics are indispensable objects in many fields, including technology and social science. This book covers recent mathematical theories and techniques to analyze such nonlinear partial differential equations.
Partial Differential Equations In Action
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Author : Sandro Salsa
language : en
Publisher: Springer
Release Date : 2015-04-24
Partial Differential Equations In Action written by Sandro Salsa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Principles Of Partial Differential Equations
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Author : Alexander Komech
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-05
Principles Of Partial Differential Equations written by Alexander Komech and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-05 with Mathematics categories.
This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.
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.
Nonlinear Pdes
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Author : Guido Schneider
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-10-26
Nonlinear Pdes 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 Mathematics 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.
Partial Differential Equations
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Author : Deborah E. Richards
language : en
Publisher: Nova Science Publishers
Release Date : 2015
Partial Differential Equations written by Deborah E. Richards and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.
Essential Partial Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer
Release Date : 2015-09-24
Essential Partial Differential Equations written by David F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Handbook Of First Order Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2001-11-15
Handbook Of First Order Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-15 with Mathematics categories.
This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding types of differential equations are outlined and specific examples are considered. It presents equations and their applications, including differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. This handbook is an essential reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences.