Introduction to the speaker: Dr. Zhu Changjiang, professor and doctoral supervisor of South China University of Technology.

Abstract: In this talk, we will introduce the asymptotic stability of solution to an Initial-boundary value problem for a hyperbolic-elliptic coupling system on two- dimensional half space. We show that the solution to the problem converges to the corresponding planar rarefaction wave as time tends to infinity. To our knowledge, the stability results of planar rarefaction wave on half space focus primarily on the single viscosity conservation law because the rarefaction wave (one-dimensional diffusion wave) of the corresponding one-dimensional problem to scalar viscosity conservation law is known. In other words, for a general high dimensional system of equations, we cannot obtain the stability of planar rarefaction wave on half space because we cannot construct the rarefaction wave of the corresponding one- dimensional problem. In this paper, we use the structure of the hyperbolic-elliptic coupling system to obtain the monotonic rarefaction wave of the corresponding one-dimensional problem, and hence give the stability of the plane rarefaction wave on half space.

School of Mathematics and Computer Sciences, Nanchang University

Sep 9, 2022