Mathematical Study for Approximation Models in Radiation Hydrodynamics

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The importance of thermal radiation in physical problems increases as the temperature is raised. At moderate temperatures, the role of the radiation is primarily one of transporting energy by radiative process, while at higher temperature, the energy and momentum densities of the radiation field may become comparable to or even dominate the corresponding field quantities. In radiation hydrodynamics, due to the presence of radiation, the classical "material" flow has to be coupled with radiation which is an assembly of photons (the photons are massless particles traveling at the speed of light) and need a priori a relativistic treatment. Hence, the whole problem to be considered is then a coupling between the standard hydrodynamics for the matter and a radiative transfer equation (also called the transport equation) for the photon distribution. This book offers our recently results on the qualitive properties like the existence, asymptotic behaviour and low Mach number limit of solutions for some compressible radiative hydrodynamic equations.