A reaction–diffusion system with fast reversible reaction

We consider a reaction–diffusion system which models a fast reversible reaction between two mobile reactants and prove convergence of the solutions as the reaction rate tends to infinity, where the limiting problem is given by a diffusion equation with nonlinear diffusion. Since the rate function has no sign, the usual methods to obtain a priori estimates in the case of irreversible reactions do not apply; we deduce instead a priori estimates from computations based on Lyapunov function techniques.  2003 Elsevier Inc. All rights reserved