Weak and Classical Solutions for a Model Problem in Radiation Hydrodynamics

Summary. It has been observed for a long time that radiation effects can prevent the development of singularities of shock-wave type in solutions for mathematical models for compressible flows. We consider a multi-dimensional model problem in the form of a system of nonlinear hyperbolic balance laws and prove that the associated Cauchy problem can have smooth global solutions provided that the initial data is sufficiently close to an equilibrium state. Numerical experiments confirm this result but also show that shock-waves can develop for large amplitude initial data.