stability for systems

of hyperbolic conservation laws

Authors:
Tai-Ping Liu and Tong Yang

Journal:
J. Amer. Math. Soc. **12** (1999), 729-774

MSC (1991):
Primary 35L67, 76L05; Secondary 35L65, 35A05

Published electronically:
April 13, 1999

MathSciNet review:
1646841

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study the evolution of the distance of solutions for systems of hyperbolic conservation laws. For the approximate solutions constructed by Glimm's scheme with the aid of the wave tracing method, we introduce a nonlinear functional which is equivalent to the distance between solutions, nonincreasing in time, and expressed explicitly in terms of the wave patterns of the solutions. This functional reveals the nonlinear mechanism of wave interactions and coupling which affect the topology.

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Additional Information

**Tai-Ping Liu**

Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305-2060

Email:
liu@math.stanford.edu

**Tong Yang**

Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

Email:
matyang@cityu.edu.hk

DOI:
http://dx.doi.org/10.1090/S0894-0347-99-00292-1

Received by editor(s):
March 8, 1998

Received by editor(s) in revised form:
September 9, 1998

Published electronically:
April 13, 1999

Additional Notes:
The first author’s research was supported in part by NSF Grant DMS-9623025

The second author’s research was supported in part by the RGC Competitive Earmarked Research Grant 9040290

Article copyright:
© Copyright 1999
American Mathematical Society