Institute of Mathematics for Industry


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Asymptotic stability of a rarefaction wave for symmetric hyperbolic-parabolic systems

Hold Date 2017-06-23 15:30~2017-06-23 17:00

Place 2nd floor room D, Seminar House, Fukuoka University

Object person  

Speaker Shinya NISHIBATA (Tokyo Institute of Technology)

In the present talk, we discuss a large time behavior of a solution to a coupled system of viscous and inviscid conservation laws. Mainly, we talk about an asymptotic stability of a rarefaction wave, with assuming an existence of an entropy function. This condition enables us to transform the original system to a normal symmetric system, which is a coupled system of hyperbolic and parabolic equations. In asymptotic analysis, we derive an a priori estimate by an energy method. Especially in deriving the basic estimate, we make use of an energy form, which is defined by substituting a smoothed rarefaction wave in the entropy function. The symmetric system is utilized in deriving higher order estimates of the derivatives of solutions. In this procedure, we have to suppose that the stability condition hold at spatial far field.