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A reaction-diffusion system approximation of a one-phase Stefan problem. (English) Zbl 1054.35019
Menaldi, José 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].

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