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Delta-waves for Semilinear Hyperbolic Cauchy Problems

โœ Scribed by Michael Oberguggenberger; Ya-Guang Wang

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
538 KB
Volume
166
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

This paper deals with the propagation of strong singularities for constant coefficient semilinear hyperbolic equations and systems. Limits of regularized solutions are computed as the initial data converge to derivatives of Dirac measures on lower dimensional submanifolds. A general method is given which applies whenever the fundamental solution to the principal part is an integrable measure. Particular cases are semilinear first order systems in one space variable and the semilinear Klein-Gordon equation in at most three space variables.

๐Ÿ“œ SIMILAR VOLUMES

Cauchy Problem for One-Dimensional Semil
Cauchy Problem for One-Dimensional Semilinear Hyperbolic Systems: Global Existence, Blow Up
โœ Denise Aregba-Driollet; Bernard Hanouzet ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 962 KB

We study the blow up or global existence of the solutions of the Cauchy problem for 2\_2 one-dimensional first order semilinear strictly hyperbolic systems with homogeneous quadratic interaction. Two characterizations are obtained: global existence for locally bounded data, global existence for smal

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โœ Marco Cappiello; Luisa Zanghirati ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 187 KB

## Abstract We study the Cauchy problem for a class of quasilinear hyperbolic systems with coefficients depending on (__t__, __x__) โˆˆ [0, __T__ ] ร— โ„^__n__^ and presenting a linear growth for |__x__ | โ†’ โˆž. We prove wellโ€posedness in the Schwartz space __๐’ฎ__ (โ„^__n__^ ). The result is obtained by d