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September 2010 Asymptotic Stability of Viscous Shock Wave for a Onedimensional Isentropic Model of Viscous Gas with Density Dependent Viscosity
Akitaka Matsumura, Yang Wang
Methods Appl. Anal. 17(3): 279-290 (September 2010).

Abstract

In this paper we investigate the asymptotic stability of viscous shock wave for a onedimensional isentropic model of viscous gas with density dependent viscosity by a weighted energy method developed in the papers of Matsumura-Mei (1997) and Hashimoto-Matsumura (2007). Under the condition that the viscosity coefficient is given as a function of the absolute temperature which is determined by the Chapman-Enskog expansion theory in rarefied gas dynamics, any viscous shock wave is shown to be asymptotically stable for small initial perturbations with integral zero. This generalizes the previous result of Matsumua-Nishihara (1985) where the viscosity coefficient is given by a constant and a restriction on the strength of the viscous shock wave is assumed. This also analytically assures the spectral stability in the Zumbrun’s theory for any viscous shock wave in our specific case.

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Akitaka Matsumura. Yang Wang. "Asymptotic Stability of Viscous Shock Wave for a Onedimensional Isentropic Model of Viscous Gas with Density Dependent Viscosity." Methods Appl. Anal. 17 (3) 279 - 290, September 2010.

Information

Published: September 2010
First available in Project Euclid: 23 May 2011

zbMATH: 1242.76059
MathSciNet: MR2785875

Subjects:
Primary: 35B40 , 35Q30 , 76N10

Keywords: Asymptotic stablility , viscous gas , viscous shock wave

Rights: Copyright © 2010 International Press of Boston

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Vol.17 • No. 3 • September 2010
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