Simultaneous null controllability of parabolic equations with nonlocal terms
Résumé
This paper is concerned with a null controllability problem for nonlinear parabolic equations appearing in mathematical biology. We consider a system of two equations with a nonlocal nonlinearity, in a bounded domain Ω of ℝN0, N0 being a positive integer sufficiently small. Such models can be used in the context of dynamics of biological systems to describe the migration of population (of bacteria in a container). Our aim is to find a control common to both equations, which solves the null controllabillity of the studied system under constraints on the state. A similar control problem has recently been addressed for the Laplace operator, so the present paper extends those results.