Analytical solutions of model kinetic radiative transfer equations and energy equation

A model system consisting of nonstationary kinetic equations of thermal radiative transfer and the energy equation in the multigroup isotropic approximation for media with constant absorption coefficients and a piecewise constant Planck function in the groups is considered. For the model system of equations, analytical solutions are obtained in the case of plane geometry and a ball. The analytical solutions are obtained by reducing the initial complicated system to a simpler one with a known analytical solution. The inverse transition yields the solution of the complicated system. Solutions of test problems for a plane layer and a ball are presented.