[PDF] Nonlinear Evolution Equations Global Behavior Of Solutions eBook

Author : Reinhard Racke
Publisher : Birkhäuser
Page : 315 pages
File Size : 46,15 MB
Release : 2015-08-31
Category : Mathematics
ISBN : 3319218735

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This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

Author : Songmu Zheng
Publisher : CRC Press
Page : 302 pages
File Size : 39,77 MB
Release : 2004-07-08
Category : Mathematics
ISBN : 1135436479

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Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, the global existence and uniqueness theory for small initial data, and the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.

Author : Tatsien Li
Publisher : World Scientific
Page : 334 pages
File Size : 24,30 MB
Release : 1999-08-31
Category :
ISBN : 9814543446

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This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.

Author : Gaston M. N'Guerekata
Publisher : Nova Publishers
Page : 258 pages
File Size : 43,42 MB
Release : 2008
Category : Mathematics
ISBN : 9781604562262

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This book presents high-quality research from around the world on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. The book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations.

Author : Pavel Ivanovich Naumkin
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 48,31 MB
Release :
Category : Science
ISBN : 9780821887691

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This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.

Author : Reinhard Racke
Publisher : Vieweg+Teubner Verlag
Page : 260 pages
File Size : 19,92 MB
Release : 2014-04-22
Category : Mathematics
ISBN : 9783663106319

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This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.

Author : Tatsien Li
Publisher : World Scientific
Page : 286 pages
File Size : 42,65 MB
Release : 1997-01-04
Category :
ISBN : 9814546429

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This volume contains 30 research papers presenting the recent development and trend on the following subjects: nonlinear hyperbolic equations (systems); nonlinear parabolic equations (systems); infinite-dimensional dynamical systems; applications (free boundary problems, phase transitions, etc.).

Author : Nina B. Maslova
Publisher : World Scientific
Page : 210 pages
File Size : 31,61 MB
Release : 1993
Category : Mathematics
ISBN : 9789810211622

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The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.