A kinetic reaction model: decay to equilibrium and macroscopic limit

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.