Singular perturbations for a semilinear hyperbolic equation

The Cauchy problem for a semilinear hyperbolic equation with a small parameter is considered. The reduced problem is of parabolic type and, although there is no reduction of order, there is an initial layer. An asymptotic solution with boundary layer corrections is constructed and, for a restricted...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 14; no. 6; pp. 1168 - 1179
Main Authors HSIAO, G. C, WEINACHT, R. J
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1983
Subjects
Applied mathematics
Estimates
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Partial differential equations
Physics
Semi linear equation
Singular perturbation
Partial differential equation
Hyperbolic equation
Cauchy problem
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Summary:The Cauchy problem for a semilinear hyperbolic equation with a small parameter is considered. The reduced problem is of parabolic type and, although there is no reduction of order, there is an initial layer. An asymptotic solution with boundary layer corrections is constructed and, for a restricted class of nonlinearities, is shown to be uniformly asymptotically valid for sets bounded in the time direction.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0036-1410
1095-7154
DOI:10.1137/0514091