A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics (Q2758112)

The singular limit of solutions to the initial value problem for a certain class of hyperbolic-elliptic coupled systems is discussed. A typical example of this problem appears in radiation hydrodynamics. It is shown that the singular limit problem of the hyperbolic-elliptic system corresponds to the concrete physical problem of making the Boltzmann number infinitesimal and the Bouguer number infinite, with their product kept constant. The solution to the hyperbolic-elliptic coupled system converges to the solution of the corresponding hyperbolic-parabolic coupled system. First, the global existence is proved by the uniform estimate which is obtained through the standard energy method. The convergence of the solution is proved.