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A reaction-diffusion system approximation of a one-phase Stefan problem. (English) Zbl 1054.35019
Menaldi, JosĂ© Luis (ed.) et al., Optimal control and partial differential equations. In honour of Professor Alain Bensoussan’s 60th birthday. Proceedings of the conference, Paris, France, December 4, 2000. Amsterdam: IOS Press; Tokyo: Ohmsha (ISBN 1-58603-096-5; 4-274-90412-1). 156-170 (2001).
Summary: 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.
For the entire collection see [Zbl 1053.49001].

35K57 Reaction-diffusion equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.