Partial null controllability of parabolic linear systems by m forces

Farid Ammar-Khodja (1) , Franz Chouly (1) , Michel Duprez (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain Ω in R N (N ∈ N *), we study the effect of m localized controls in a nonempty open subset ω only controlling p components of the solution (p, m n). The first main result of this paper is a necessary and sufficient condition when the coupling and control matrices are constant. The second result provides, in a first step, a sufficient condition of partial null controllability when the matrices only depend on time. In a second step, through an example of partially controlled 2 × 2 parabolic system, we will give positive and negative results on partial null controllability when the coefficients are space dependent.

Mots clés: Null controllability; Approximate controllability; Parabolic systems

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]

Farid Ammar-Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems by m forces. 2015. ⟨hal-01115812v1⟩