Stabilization strategies for some reaction-diffusion systems

Sebastian Anita , 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

A two-component reaction-diffusion system is considered. The question of stabilizing to zero one of the components of the solution via an internal control acting on a small subdomain and preserving nonnegativity of both components is investigated. Our results apply to predator-prey systems

Keywords: Reaction-diffusion system; internal stabilization; comparison principle; predator-prey system

Domains: Analysis of PDEs [math.AP]; Ecology, environment

Sebastian Anita, Michel Langlais. Stabilization strategies for some reaction-diffusion systems. Nonlinear Analysis: Real World Applications, 2009, 10, pp.345-357. ⟨10.1016/j.nonrwa.2007.09.003⟩. ⟨hal-00269161⟩