## Diffusion in the Presence of Fast Reaction: the Case of a General Monotone Reaction Term

J. Math. Sci. Univ. Tokyo
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
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.