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This paper studies the asymptotic stability of solution to aninitial-boundary value problem for a hyperbolic-elliptic coupled system ontwo-dimensional half space, where the data on the boundary and at the far fieldare prescribed as $u_-$ and $u_+$. We show that the solution to the problemconverges to the corresponding planar rarefaction wave for $0\le u_-<u_+$ astime tends to infinity under smallness assumptions on the initial perturbationand wave strength. These results are based on the analysis of div-curldecomposition, the standard $L^2$-energy method, $L^1$-estimate, and themonotonicity of profile is given by the maximum principle.

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