On a constrained reaction-diffusion system related to multiphase problems

José-Francisco Rodrigues; Lisa Santos

doi:10.3934/dcds.2009.25.299

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2009, Volume 25, Issue 1: 299-319. Doi: 10.3934/dcds.2009.25.299

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On a constrained reaction-diffusion system related to multiphase problems

José-Francisco Rodrigues^1, and
Lisa Santos^2,

1.
CMAF/Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa
2.
Universidade do Minho/CMat, Campus de Gualtar, 4710 - 057 Braga

Received: October 2007

Revised: May 2008

Published: January 2009

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Abstract

We solve and characterize the Lagrange multipliers of a reaction-diffusion system in the Gibbs simplex of $\R^{N+1}$ by considering strong solutions of a system of parabolic variational inequalities in $\R^N$. Exploring properties of the two obstacles evolution problem, we obtain and approximate a $N$-system involving the characteristic functions of the saturated and/or degenerated phases in the nonlinear reaction terms. We also show continuous dependence results and we establish sufficient conditions of non-degeneracy for the stability of those phase subregions.

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Mathematics Subject Classification: Primary: 35K57, 35K85; Secondary: 35R35, 74N25, 91A99, 92D99.

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