Diffusion in the Presence of Fast Reaction: the Case of a General Monotone Reaction Term
Vol. 4 (1997), No. 3, Page 469--517.
Hilhorst, D. ; van der Hout, R. ; Peletier, L. A.
Diffusion in the Presence of Fast Reaction: the Case of a General Monotone Reaction Term
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Abstract:
We study here a reaction-diffusion system involving a mobile reactant $(u)$ and an immobile reactant $(v)$ under the assumption that the reaction kinetics is monotone with respect to $u$ and $v$. We prove a general global existence and uniqueness theorem and show that in the limit of fast reaction, the solution $(u,v)$ converges to the solution $(\ou,\ov)$ of a simpler limit problem. When the solution $(u,v)$ has a free boundary, as is the case when dead cores occur, we study the limiting behaviour of these boundaries. This paper extends an earlier one in which the reaction-diffusion system had the special property that it could be transformed to a single diffusion equation.
Mathematics Subject Classification (1991): 35K57, 35B25, 35B40
Mathematical Reviews Number: MR1484599
Received: 1996-06-07
