Global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms

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Original languageEnglish
Pages (from-to)1311-1324
Journal / PublicationRoyal Society of Edinburgh - Proceedings A
Volume127
Issue number6
Publication statusPublished - 1997

Abstract

In this paper we prove an existence theorem of global smooth solutions for the Cauchy problem of a class of quasilinear hyperbolic systems with nonlinear dissipative terms under the assumption that only the C0-norm of the initial data is sufficiently small, while the C1-norm of the initial data can be large. The analysis is based on a priori estimates, which are obtained by a generalised Lax transformation.