Investigation of a mathematical model for radiation hydrodynamics (Q1818883)

A system is considered which describes the radiation propagation through a continuum. The reduction to a symmetric \(t\)-hyperbolic system via the symmetrization procedure is done under the assumption that an additional conservation law is valid for the solutions of the system. Then a global existence theorem for the Cauchy problem is proved when initial data are close to zero. Jump conditions are derived for the solutions with shocks, and the shock wave stability problem is studied.