Hyperbolic-hyperbolic relaxation limit for a 1D compressibleradiation hydrodynamics model: superposition of rarefaction  andcontact waves

Christian Rohde; Wenjun Wang; Feng Xie

doi:10.3934/cpaa.2013.12.2145

Article Contents

2013, Volume 12, Issue 5: 2145-2171. Doi: 10.3934/cpaa.2013.12.2145

This issue Previous Article Approximation of the trajectory attractor of the 3D MHD System Next Article The Fractional Ginzburg-Landau equation with distributional initial data

Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves

1.
Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart
2.
College of Science, University of Shanghai for Science and Technology, Shanghai 200240
3.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Received: April 30, 2012

Revised: July 31, 2012

Published: August 2013

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Abstract

In this paper we consider a hyperbolic-hyperbolic relaxation limit problem for a 1D compressible radiation hydrodynamics (RHD) system. The RHD system consists of the full Euler system coupled with an elliptic equation for the radiation flux. The singular relaxation limit process we consider corresponds to the physical problem of letting the Bouguer number become infinite. We prove for appropriate initial datum that the solution of the initial value problem for the RHD system converges for vanishing reciprocal Bouguer number to a weak solution of the limit system which is the Euler system. The initial data are chosen such that the limit solution is composed by a $1$-rarefaction wave, a contact discontinuity and a $3$-rarefaction wave. Moreover we give the convergence rate in terms of the physical parameter.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35L03, 35L65.

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