Special Session 95: 

Asymptotic stability of a rarefaction wave for a symmetric system of hyperbolic-parabolic coupled equations

Shinya Nishibata
Tokyo Institute of Technology
Japan
Co-Author(s):    Tetsuya Mitsuhori, Tohru Nakamura
Abstract:
In this talk we discuss a large time behavior of a solution to a coupled system of viscous and inviscid conservation laws. The system of equations appears in compressible fluid dynamics. We, mainly, talk about an asymptotic stability of a rarefaction wave under assuming the existence of an entropy function. This assumption enables us to rewrite the original system in a normal form consisted of symmetric hyperbolic and parabolic systems. In asymptotic analysis, we derive an a priori estimate by an energy method. In order to derive the basic estimate, we make use of an energy form defined by substituting a smooth approximation of the rarefaction wave in the entropy function. The symmetric system is utilized in deriving the estimates of the higher order derivatives of the solution. In this computation, we suppose the stability condition, which ensures dissipation.