  This work pursues two main directions, the derivation of a reaction diffusion
equation from a kinetic reaction model, and the exponential convergence of the
nonlinear kinetic system towards the global equilibrium through the
hypocoercivity techniques. The model describes the evolution of two species,
which are subject to transport, thermalization, and second order reaction. The
nonlinearity arises from the mass action law, i.e.~the product of the reactants
distribution.
