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On a constrained reaction-diffusion system related to multiphase problems

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

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