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

José-Francisco Rodrigues; João Lita da Silva

doi:10.3934/cpaa.2004.3.85

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2004, Volume 3, Issue 1: 85-95. Doi: 10.3934/cpaa.2004.3.85

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

José-Francisco Rodrigues^1, and
João Lita da Silva^2,

1.
CMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa
2.
Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica

Received: October 31, 2002

Revised: May 31, 2003

Published: February 2004

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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.

Keywords:

Reaction-diffusion system,
nonlocal evolution obstacle problems.

Mathematics Subject Classification: 35R35, 35K85.

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