Diffusion asymptotics of a coupled model for radiative transfer in a unit disk (Q6155286)

The authors consider a spatial two-dimensional boundary value problem for radiative transfer. The specific intensity of radiation (a function of time, point, and direction) is governed by a kinetic equation, material temperature (a function of time and point) obeys the drift-diffusion equation, with a given velocity field. The domain is the unit disk. The small parameter appears as a factor in the kinetic equation, turning off the black-body radiation dependent on the temperature. Thus, in the limit case, the kinetic equation is decoupled from the temperature. Boundary conditions are of the Dirichlet type. The focus is on asymptotic analysis of the behaviour of the solutions as the small parameter tends to zero. The result is that an \(L^\infty\) Sobolev-type solution exists, is unique, and converges (in \(L_2\) or \(C_0\), depending on the variable) to the solution to the limit problem. The smoothness requirement for the boundary and initial data is \(C_6\) or \(C_8\).