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On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem

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  • 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.
    Mathematics Subject Classification: 35R35, 35K85.


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