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February  2009, 25(1): 299-319. doi: 10.3934/dcds.2009.25.299

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, Portugal

Received  October 2007 Revised  May 2008 Published  June 2009

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.
Keywords: Reaction-diffusion systems, multiphase problems, parabolic variational inequalities, evolutionary game dynamics..
Mathematics Subject Classification: Primary: 35K57, 35K85; Secondary: 35R35, 74N25, 91A99, 92D9.
Citation: José-Francisco Rodrigues, Lisa Santos. On a constrained reaction-diffusion system related to multiphase problems. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 299-319. doi: 10.3934/dcds.2009.25.299
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