Extended Boltzmann equations for light particles reacting with a medium

We consider two species of light test particles interacting with a medium constituted by two species of much heavier field particles. A reversible bimolecular chemical reaction is assumed to occur, with conservation of mass, momentum and total energy. In the Lorentz gas limit, the resulting model is described by a system of two extended linear Boltzmann equations for the light test particles. The main properties of the collision operators are discussed and collision invariants are properly introduced. Equilibria are determined and turn out to be defined up to an arbitrary isotropic shape function. Stability and uniqueness of the equilibrium associated to any given initial datum are investigated in the space homogeneous case.