stability for systems of hyperbolic conservation laws
Authors:
TaiPing Liu and Tong Yang
Journal:
J. Amer. Math. Soc. 12 (1999), 729774
MSC (1991):
Primary 35L67, 76L05; Secondary 35L65, 35A05
Published electronically:
April 13, 1999
MathSciNet review:
1646841
Fulltext PDF Free Access
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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
TaiPing Liu
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 943052060
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/S0894034799002921
PII:
S 08940347(99)002921
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 DMS9623025
The second author’s research was supported in part by the RGC Competitive Earmarked Research Grant 9040290
Article copyright:
© Copyright 1999 American Mathematical Society
