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

Published online by Cambridge University Press:  14 November 2011

Tong Yang ,
Changjiang Zhu  and
Huijiang Zhao
Tong Yang
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Changjiang Zhu
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong; Wuhan Institute of Mathematical Sciences, Chinese Academy of Sciences, Wuhan 430071, P. R. China
Huijiang Zhao
Affiliation:
Wuhan Institute of Mathematical Sciences, Chinese Academy of Sciences, Wuhan 430071, P.R. China
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Extract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 6 , 1997 , pp. 1311 - 1324
Copyright
Copyright © Royal Society of Edinburgh 1997

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