๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Cauchy problem for quasilinear SG-hyperbolic systems

โœ Scribed by Marco Cappiello; Luisa Zanghirati

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
187 KB
Volume
280
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 deriving an energy estimate for the solution of the linearized problem in some weighted Sobolev spaces and applying a fixed point argument. (ยฉ 2007 WILEYโ€VCH Verlag GmbH & Co. KGaA, Weinheim)

๐Ÿ“œ SIMILAR VOLUMES

Generalized Solutions to a Cauchy Proble
Generalized Solutions to a Cauchy Problem for a Nonconservative Hyperbolic System
โœ K.T. Joseph ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 323 KB

In this paper we show the existence of generalized solutions, in the sense of Colombeau, to a Cauchy problem for a nonconservative system of hyperbolic equations, which has applications in elastodynamics.

The Mixed Dirichletโ€“Neumannโ€“Cauchy Probl
The Mixed Dirichletโ€“Neumannโ€“Cauchy Problem for Second Order Hyperbolic Operators
โœ Joseph Bennish ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 224 KB

A hyperbolic mixed initial boundary-value problem is investigated in which the Neumann condition and the Dirichlet condition are given on complementary parts of the boundary. An existence and uniqueness result in Sobolev spaces with additional differentiation in the tangential directions to the inte