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

Xin, Zhou Ping

doi:10.1090/S0002-9947-1990-0970270-8

Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions
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Trans. Amer. Math. Soc. 319 (1990), 805-820 Request permission

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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Linear and quasi-linear equations of parabolic type