  We propose a kinetic relaxation-model to describe a generation-recombination
reaction of two species. The decay to equilibrium is studied by two recent
methods for proving hypocoercivity of the linearized equations. Exponential
decay of small perturbations can be shown for the full nonlinear problem. The
macroscopic/fast-reaction limit is derived rigorously employing entropy decay,
resulting in a nonlinear diffusion equation for the difference of the position
densities.

Analysis of PDEs