The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction

Dieter Bothe (1) , Michel Pierre (2)

1 Mathematical Modeling and Analysis
2 IRMAR - Institut de Recherche Mathématique de Rennes

We consider reaction-diffusion systems which, in addition to certain slow reactions, contain a fast irreversible reaction in which chemical components A and B form a product P. In this situation and under natural assumptions on the RD-system we prove the convergence of weak solutions, as the reaction speed of the irreversible reaction tends to infinity, to a weak solution of a limiting system. The limiting system is a Stefan-type problem with a moving interface at which the chemical reaction front is localized.

Mots clés: Chemical reaction interface; instantaneous chemical reaction; spatial segregation; Stefan-type problem

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Dieter Bothe, Michel Pierre. The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction. Discrete and Continuous Dynamical Systems - Series S, 2012, 5 (1), pp.49-59. ⟨10.3934/dcdss.2012.5.49⟩. ⟨hal-00685755⟩