On a constrained reaction-diffusion system related to a multiphase problem

• Author(s): Rodrigues, José Francisco ; Santos, Lisa
• Date: 2009
• Persistent ID: http://hdl.handle.net/1822/9738
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Reaction-diffusion systems; Multiphase problems; Parabolic variational inequalities; Evolutionary game dynamics
• Document Type: Article
• Language: English

Description

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.