Convergence toward Equilibrium for Chemical Reaction Diffusion Systems

Résumé : We consider the asymptotic behavior of solutions for reaction-diffusion system modeling reversible reaction process. In this talk, especially, we focus on the case that the chemical species are not separated. In this case, due to the existence of boundary equilibria, the analysis of the asymptotic behavior becomes difficult. After constructing “solutions” which is understood as any limit of adequate approximate solutions, we prove this solution converges toward an equilibrium as time goes to infinity. We also give a sufficient condition which assures this equilibrium is the strictly positive equilibrium. Then, this convergence become exponential.
This is joint work with Michel Pierre (ENS Rennes).