Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves
Hyperbolic-hyperbolic relaxation limit for a 1D compressible radiation hydrodynamics model: superposition of rarefaction and contact waves
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DOI：
10.3934/cpaa.2013.12.2145
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发表时间：
2013
影响因子：
1
通讯作者：
C. Rohde;Wenjun Wang;Feng Xie
中科院分区：
文献类型：
--
作者：
C. Rohde;Wenjun Wang;Feng Xie
本文研究一维可压缩辐射流体动力学系统的双曲-双曲松弛极限问题。RHD系统由全欧拉系统和辐射通量的椭圆方程耦合组成。我们所考虑的奇异松弛极限过程对应于布格数无穷化的物理问题。在适当的初始基准下，证明了RHD系统初值问题的解收敛于消失倒数布格数的极限系统即欧拉系统的一个弱解。选择初始数据，使极限解由$1$稀疏波、$3$稀疏波和$1$稀疏波组成。并给出了用物理参数表示的收敛速率。
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.