An exact solution for the linearized multifrequency radiation diffusion equation

An exact solution, based on Fourier and Laplace (FL) transforms, is developed for a linearization of the system modeling the multifrequency radiation diffusion and matter energy balance equations. The model uses an ideal gas equation of state. Opacities are proportional to the inverse of the cube of the frequency, thereby simulating free-free transitions. The solution is obtained in terms of integrals over the FL coefficients of the initial conditions and explicit sources. Results are presented for two special cases. (1) No sources, initially cold radiation field, and a localized matter energy profile. (2) Initially cold matter and radiation fields and a source of matter energy extending over finite space and time intervals.