On a quantum Boltzmann equation for a gas of photons.
In this article the existence and uniqueness of the solution and its convergence to equilibrium are proved for the nonlinear spatially homogeneous quantum Boltzmann equation describing Compton electron-photon scattering. Apart from trivial factors occurring naturally the collision term is assumed to be of convolution type in the wave number with a positive convolution kernel. A thorough study of the stationary solutions and the entropy dissipation term are made. A rigorous proof is given to show that the Kompaneets equation occurs as the Fokker-Planck type limit of the Boltzmann equation studied.
scientific article; zbMATH DE number 1770834
scientific article