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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 970270
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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 $ {L^2}$-energy method.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0970270-8
PII: S 0002-9947(1990)0970270-8
Keywords: Nonlinear stable, viscous conservation law, planar rarefaction wave, $ {L^2}$-energy method
Article copyright: © Copyright 1990 American Mathematical Society