Asymptotic stability of viscous contact wave for the inflow problem of the one-dimensional radiative Euler equations

Lili Fan; Lizhi Ruan; Wei Xiang

doi:10.3934/dcds.2020349

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2021, Volume 41, Issue 4: 1971-1999. Doi: 10.3934/dcds.2020349

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Asymptotic stability of viscous contact wave for the inflow problem of the one-dimensional radiative Euler equations

1.
School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China
2.
Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
3.
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

^* Corresponding author: Lizhi Ruan, rlz@mail.ccnu.edu.cn
^* Corresponding author: Lizhi Ruan, rlz@mail.ccnu.edu.cn

Received: February 29, 2020

Revised: July 31, 2020

Early access: October 2020

Published: April 2021

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Abstract

This paper is devoted to the study of the inflow problem governed by the radiative Euler equations in the one-dimensional half space. We establish the unique global-in-time existence and the asymptotic stability of the viscous contact discontinuity solution. It is different from the case involved with the rarefaction wave for the inflow problem in our previous work [6], since the rarefaction wave is a nonlinear expansive wave, while the contact discontinuity wave is a linearly degenerate diffusive wave. So we need to take good advantage of properties of the viscous contact discontinuity wave instead. Moreover, series of tricky argument on the boundary is done carefully based on the construction and the properties of the viscous contact discontinuity wave for the radiative Euler equations. Our result shows that radiation contributes to the stabilization effect for the supersonic inflow problem.

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Mathematics Subject Classification: Primary: 35B35, 35B40, 35M30, 35Q35, 76N10; Secondary: 76N15.

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