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On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem
We prove the existence of solution to a free boundary problem of
obstacle type with a diffusion coefficient depending on a function
whose equation has a discontinuous reaction term. Our method uses
the continuous dependence properties of the coincidence set of the
evolution obstacle problem under a general non-degenerating
condition. Motivated by the oxygen consumption problem with, for
instance, temperature dependent diffusion, we obtain in a limit
case a nonlocal problem of new type, which involves the measure of
the domain occupied by the oxygen at each instant.