A Note on a Multi-Dimensional Radiating Gas Model with Nonlinear Radiative Inhomogeneity  

作　　者：CHEN Yufeng RUAN Lizhi WEI Jing 

机构地区：[1]School of Mathematics and Statistics,and Hubei Key Lab–Math.Sci.,Central China Normal University,Wuhan 430079,PR China

出　　处：《Journal of Partial Differential Equations》2024年第2期166-186,共21页偏微分方程（英文版）

基　　金：supported in part by the Natural Science Foundation of China(Nos.12171186,11771169);the grand number CCNU22QN001 of the Fundamental Research Funds for the Central Universities.

摘　　要：In this paper,we consider the Cauchy problem of a multi-dimensional radiating gas model with nonlinear radiative inhomogeneity.Such a model gives a good approximation to the radiative Euler equations,which are a fundamental system in radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena.One of our main motivations is to attempt to explore how nonlinear radiative inhomogeneity influences the behavior of entropy solutions.Simple but different phenomena are observed on relaxation limits.On one hand,the same relaxation limit such as the hyperbolic-hyperbolic type limit is obtained,even for different scaling.On the other hand,different relaxation limits including hyperbolic-hyperbolic type and hyperbolic-parabolic type limits are obtained,even for the same scaling if different conditions are imposed on nonlinear radiative inhomogeneity.

关 键 词：Radiating gas model nonlinear radiative inhomogeneity entropy solution global well-posedness relaxation limit 

分 类 号：O175.23[理学—数学] O175.28[理学—基础数学] O175.29