Reinhard Racke

(Author)

Lectures on Nonlinear Evolution Equations: Initial Value Problems (2015)Hardcover - 2015, 7 September 2015

Lectures on Nonlinear Evolution Equations: Initial Value Problems (2015)
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Print Length
306 pages
Language
English
Publisher
Birkhauser
Date Published
7 Sep 2015
ISBN-10
3319218727
ISBN-13
9783319218724

Description

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.

Product Details

Author:
Reinhard Racke
Book Edition:
2015
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
7 September 2015
Dimensions:
23.39 x 15.6 x 1.91 cm
ISBN-10:
3319218727
ISBN-13:
9783319218724
Language:
English
Location:
Cham
Pages:
306
Publisher:
Weight:
616.89 gm

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