Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions

Author:
Zhou Ping Xin

Journal:
Trans. Amer. Math. Soc. **319** (1990), 805-820

MSC:
Primary 35L65; Secondary 76L05, 76N10

DOI:
https://doi.org/10.1090/S0002-9947-1990-0970270-8

MathSciNet review:
970270

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper concerns the large time behavior toward planar rarefaction waves of the solutions for scalar viscous conservation laws in several dimensions. It is shown that a planar rarefaction wave is nonlinearly stable in the sense that it is an asymptotic attractor for the viscous conservation law. This is proved by using a stability result of rarefaction wave for scalar viscous conservation laws in one dimension and an elementary -energy method.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-0970270-8

Keywords:
Nonlinear stable,
viscous conservation law,
planar rarefaction wave,
-energy method

Article copyright:
© Copyright 1990
American Mathematical Society