On the solvability of the transfer equation coupled with Boltzmann equation for two-level atoms

We consider the nonlinear transfer equation coupled with the Boltzmann equation for two-level atoms in plane-parallel semi-infinite medium. It is assumed that the velocity distributions of atoms in the ground and excited states are different from the Maxwell distribution. This assumption is justified by the selective nature of the excitation of atoms by photons of different frequencies. In the linear approximation the problem is reduced to the Wiener-Hopf equation with a dissipative kernel. We prove the existence of a positive, bounded and integrable solution in the quasilinear approximation. We also obtain two-sided estimates for the source function.