Abstract
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.
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