-stability of stationary discrete shocks

Authors:
Jian-Guo Liu and Zhou Ping Xin

Journal:
Math. Comp. **60** (1993), 233-244

MSC:
Primary 35L65; Secondary 35L67, 65M12

MathSciNet review:
1159170

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Abstract | References | Similar Articles | Additional Information

Abstract: The nonlinear stability in the -norm, , of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1993-1159170-7

Keywords:
Lax-Friedrichs scheme,
hyperbolic systems of conservation laws,
discrete shock profiles,
nonlinear stability

Article copyright:
© Copyright 1993
American Mathematical Society