A fast precipitation and dissolution reaction for a reaction–diffusion system arising in a porous medium

This paper is devoted to the study of a fast reaction–diffusion system arising in reactive transport. It extends the articles R. Eymard, T. Gallouët, R. Herbin, D. Hilhorst, M. Mainguy, Instantaneous and noninstantaneous dissolution: Approximation by the finite volume method, ESAIM Proc. (1998); J. Pousin, Infinitely fast kinetics for dissolution and diffusion in open reactive systems, Nonlinear Anal. 39 (2000) 261–279] since a precipitation and dissolution reaction is considered so that the reaction term is not sign-definite and is moreover discontinuous. Energy type methods allow us to prove uniform estimates and then to study the limiting behavior of the solution as the kinetic rate tends to infinity in the special situation of one aqueous species and one solid species.