Infinitely fast kinetics for dissolution and diffusion in open reactive systems. (English) Zbl 0939.35040

Pousin, J.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 39, No. 3, 261-279 (2000).

In the present paper it is analysed the asymptotics of the dissolution-diffusion reactive model that consists of a mixed system of two semilinear partial differential equations (a parabolic one and a hyperbolic one) with jumping nonlinearities. It is introduced the function \(Z\) (Legendre function) associated to the concentration in liquid phase, and convergence results for this function, when \(k\) (the rate of dissolution) becomes infinite, are given. It is proved also that the sequence of functions representing the concentration in liquid phase converges to the solution of a Stefan problem when \(k\) goes to infinity.

Reviewer: Costică Moroşanu (Iaşi)

MSC:

35C20	Asymptotic expansions of solutions to PDEs
35R35	Free boundary problems for PDEs

Keywords:

parabolic-hyperbolic system; jumping nonlinearities