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 funda...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.展开更多
We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu...We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.展开更多
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.
文摘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.
基金The research was supported by the National Natural Science Foundation of China #10625105 and #10431060, the Program for New Century Excellent Talents in University #NCET-04-0745. Acknowledgement Authors would like to thank the anonymous referee for his/her helpful suggestions and comments.
文摘We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.
