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Journal Articles Mathematical Control and Related Fields Year : 2017

Partial null controllability of parabolic linear systems

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.
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Dates and versions

hal-01115812 , version 1 (11-02-2015)
hal-01115812 , version 2 (24-02-2016)

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Farid Ammar-Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems. Mathematical Control and Related Fields, 2017, 6 (2), pp.Pages: 185 - 216. ⟨10.3934/xx.xx.xx.xx⟩. ⟨hal-01115812v2⟩
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