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Abstract : 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.

Keywords : Null controllability Approximate controllability Parabolic systems





Author: Farid Ammar-Khodja - Franz Chouly - Michel Duprez -

Source: https://hal.archives-ouvertes.fr/



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