Asymptotic stability of rarefaction wave for the inflow problem governed by the one-dimensional radiative Euler equations. (English) Zbl 1412.35239
Summary: This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic equation. In particular, we focus our attention on the inflow problem when the velocity of the inward flow on the boundary is given as a positive constant. We give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength, provided that the data on the boundary is supersonic. It is the first rigorous result on the initial-boundary value problem for the radiative Euler equations. New and subtle analysis is developed to overcome difficulties due to the boundary effect to derive energy estimates.
MSC:
| 35Q31 | Euler equations |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35M30 | Mixed-type systems of PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76N15 | Gas dynamics (general theory) |
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