Asymptotic stability of planar rarefaction wave to a 2D hyperbolic-elliptic coupling system of the radiating gas on half-space

  • Minyi Zhang

    South China University of Technology, Guangzhou, P. R. China
  • Changjiang Zhu

    South China University of Technology, Guangzhou, P. R. China
Asymptotic stability of planar rarefaction wave to a 2D hyperbolic-elliptic coupling system of the radiating gas on half-space cover

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Abstract

This paper studies the asymptotic stability of solutions to an initial-boundary value problem for a hyperbolic-elliptic coupling system on the two-dimensional half-space, where the data on the boundary and at the far field are prescribed as and , respectively. We show that the solution to the problem converges to the corresponding planar rarefaction wave for as time tends to infinity. To the best of our knowledge, the stability results of planar rarefaction waves on half-space focus primarily on the single viscous conservation law because the rarefaction wave (one-dimensional diffusion wave) of the corresponding one-dimensional problem to scalar viscous conservation law is known. In other words, for a general high-dimensional system of equations, we cannot obtain the stability of planar rarefaction waves 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 hyperbolic-elliptic coupling system, and hence give the stability of the planar rarefaction wave on half-space. This can be viewed as the first result for the system of equations on the stability of planar rarefaction waves on half-space.

Cite this article

Minyi Zhang, Changjiang Zhu, Asymptotic stability of planar rarefaction wave to a 2D hyperbolic-elliptic coupling system of the radiating gas on half-space. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1434