Global Existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains

Sebastian Anita , W.E. Fitzgibbon , Michel Langlais (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

We consider a two-component Reaction-Diffusion system posed on non coincident spatial domains and featuring a reaction term involving an integral kernel. The question of global existence of componentwise nonnega- tive solutions is assessed. Then we investigate the stabilization of one of the solution components to zero via an internal control distributed on a small sub- domain while preserving nonnegativity of both components. Our results apply to predator-prey systems.

Mots clés: Reaction-diffusion systems; non coincident spatial domains; global existence; stabilization; principal eigenvalue; predator-prey model

Domaines: Equations aux dérivées partielles [math.AP]

Sebastian Anita, W.E. Fitzgibbon, Michel Langlais. Global Existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains. Discrete and Continuous Dynamical Systems - Series B, 2009, 11 (4), pp.805-822. ⟨10.3934/dcdsb.2009.11.xx⟩. ⟨hal-00372932⟩