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Convergence of the viscosity method for some nonlinear hyperbolic systems

Published online by Cambridge University Press:  14 November 2011

Yunguang Lu
Yunguang Lu
Affiliation:
Institute of Mathematical Sciences, Academia Sinica, P.O. Box 71007, Wuhan 430071, People's Republic of China
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Abstract

In this paper some special entropy–entropy flux pairs of Lax type are constructed for nonlinear hyperbolic systems of types (1.1) and (1.2), in which the progression terms are functions of a single variable. The necessary estimates for the major terms are obtained by the use of singular perturbation theory. The special entropies provide a convergence theorem in the strong topology for the artificial viscosity method when applied to the Cauchy problems (1.1), (1.3) and (1.2), (1.3) and used together with the theory of compensated compactness.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 2 , 1994 , pp. 341 - 352
Copyright
Copyright © Royal Society of Edinburgh 1994

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