[PDF] Global Classical Solutions For Nonlinear Evolution Equations eBook

Author : Reinhard Racke
Publisher : Birkhäuser
Page : 315 pages
File Size : 20,54 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 : 304 pages
File Size : 49,99 MB
Release : 2004-07-08
Category : Mathematics
ISBN : 0203492226

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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

Author : Tatsien Li
Publisher : World Scientific
Page : 334 pages
File Size : 23,5 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 : Tatsien Li
Publisher : World Scientific
Page : 286 pages
File Size : 18,58 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 : Wolfgang Arendt
Publisher : Birkhäuser
Page : 803 pages
File Size : 44,20 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034879245

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Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.