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

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