Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions
Author:
Zhou Ping Xin
Journal:
Trans. Amer. Math. Soc. 319 (1990), 805820
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 energy method.
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 T. P. Liu, Linear and nonlinear large time behavior of general systems of hyperbolic conservation laws, Comm. Pure Appl. Math. 30 (1977), 767796. MR 0499781 (58:17556)
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 A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, SpringerVerlag, New York, 1984. MR 748308 (85e:35077)
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 A. Mastumura, Asymptotics toward rarefaction wave of solutions of the Broadwell model of a discrete velocity gas, Japan J. Appl. Math. 4 (1987), 489502. MR 925621 (89h:35044)
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 A. Mastumura and K. Nishihara, Asymptotics toward the rarefaction waves of the solutions of a onedimensional model system for compressible viscous gas, Japan J. Appl. Math. 3 (1986), 113. MR 899210 (88e:35173)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199009702708
PII:
S 00029947(1990)09702708
Keywords:
Nonlinear stable,
viscous conservation law,
planar rarefaction wave,
energy method
Article copyright:
© Copyright 1990
American Mathematical Society
