Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions in a System of Bodies with Piecewise Smooth Boundaries

Abstract

We consider the boundary value problem for the radiative transfer equation with diffuse reflection and refraction conditions in a system of semitransparent bodies with piecewise smooth boundaries. For the problem with data in the complete scale of Lebesgue spaces we establish the existence and uniqueness of a solution. We obtain a priori estimates for the solution and show the continuous dependence of the solution on the data. The conjugate problem is also studied. Bibliography: 8 titles.