Asymptotics of diffusion-limited fast reactions

We are concerned with the fast-reaction asymptotics λ → ∞ \lambda \to \infty for a semi-linear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to λ \lambda ) L 1 L^1 -estimates for both fluxes and products of reaction and a balanced formulation , where combinations of the original components which balance the fast reaction are used.