A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics

We discuss the singular limit of solutions to the initial value problem for a certain class of hyperbolic-elliptic coupled systems. A typical example of this problem appears in radiation hydrodynamics. It is shown that the si ngular limit problem of the hyperbolic-elliptic system corresponds to the c oncrete physical problem of making the Boltzmann number become infinitesima l and the Bouguer number become infinite, with their product kept constant. We show that the solution to the hyperbolic-elliptic coupled system converg es to the solution of the corresponding hyperbolic-parabolic coupled system . First, the global existence is proved by the uniform estimate which is ob tained through the standard energy method. Then applying the uniform estima te, we prove the convergence of the solution.