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A reaction-diffusion system approximation of a one-phase Stefan problem

In this paper we study the fast reaction limit of a reaction-diffusion system, in which two reactants are involved. For a given reaction rate constant k, we establish the existence and uniqueness of the solution (u k , v k ) and prove that this solution converges to a limit (U, V) as k tends to infinity. The pair (U, V) is such UV = 0 and U - V is the weak solution of a one-phase Stefan problem.