学术报告（朱长江 7.3）

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 result of planar rarefaction wave on half space focus primarily on the single viscosity conservation law because the rarefaction wave (onedimensional 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 onedimensional 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. This is a joint work with Minyi Zhang.