In this talk, we discuss a large time behavior of a solution to a coupled system of viscous and inviscid conservation laws over one-dimensional half space. The purpose of research is to show an existence of a stationary solution and its asymptotic stability under assuming the existence of an entropy function. This assumption enables us to transform the original system to a symmetric hyperbolic-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, which is obtained by substituting the stationary solution in the entropy function. The symmetric system is utilized in deriving the estimates of the higher order derivatives of solutions. In this procedure, we suppose that the stability condition hold at spatial far field.

报告人简介: Dr. Shinya NISHIBATA is a full Professor at the Department of Mathematics and Computing Science, School of Computing, Tokyo Institute of Technology. He obtained his PhD degree in 1994 from the Department of Mathematics, Stanford University. His main research interest is evolution partial differential equations with applications.