ON A MODEL TRANSPORT-EQUATION WITH INELASTIC-SCATTERING

In the frame of extended kinetic theory, a Lorentz-type model is propo sed, which allows for inelastic scattering between a swarm of test par ticles and a background of heavy field particles. For the sake of simp licity, only two internal energy levels are considered for the backgro und molecules. After analysing the main properties of the collision op erator (null space and relaxation to equilibrium), the diffusive appro ximation is recovered as the asymptotic limit when the mean free path tends to zero, and an analytical solution in implicit form is derived for the space homogeneous problem.