Asymptotics toward the planar rarefaction wave for viscous conservation law

in two space dimensions

Authors:
Masataka Nishikawa and Kenji Nishihara

Journal:
Trans. Amer. Math. Soc. **352** (2000), 1203-1215

MSC (1991):
Primary 35L65, 35L67, 76L05

DOI:
https://doi.org/10.1090/S0002-9947-99-02290-4

Published electronically:
September 20, 1999

MathSciNet review:
1491872

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the asymptotic behavior of the solution toward the planar rarefaction wave connecting and for the scalar viscous conservation law in two space dimensions. We assume that the initial data tends to constant states as , respectively. Then, the convergence rate to of the solution is investigated without the smallness conditions of and the initial disturbance. The proof is given by elementary -energy method.

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Additional Information

**Masataka Nishikawa**

Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169, Japan

Email:
masataka@mn.waseda.ac.jp

**Kenji Nishihara**

Affiliation:
School of Political Science and Economics, Waseda University Tokyo, 169-50, Japan

Email:
kenji@mn.waseda.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-99-02290-4

Keywords:
Nonlinear stable,
viscous conservation law,
planar rarefaction wave,
$L^2$-energy method.

Received by editor(s):
July 8, 1996

Received by editor(s) in revised form:
October 14, 1997

Published electronically:
September 20, 1999

Article copyright:
© Copyright 1999
American Mathematical Society