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March  2004, 3(1): 85-95. doi: 10.3934/cpaa.2004.3.85

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, Portugal
2. 

Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

Received  November 2002 Revised  June 2003 Published  January 2004

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: nonlocal evolution obstacle problems., Reaction-diffusion system.
Mathematics Subject Classification: 35R35, 35K85. .
Citation: José-Francisco Rodrigues, João Lita da Silva. On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem. Communications on Pure and Applied Analysis, 2004, 3 (1) : 85-95. doi: 10.3934/cpaa.2004.3.85
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