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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Article dans une revue
Mathematical Control and Related Fields, AIMS, 2017, 6 (2), pp.Pages: 185 - 216. 〈http://dx.doi.org/10.3934/mcrf.2016001〉
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Soumis le : mercredi 24 février 2016 - 13:10:45
Dernière modification le : samedi 18 novembre 2017 - 00:10:56

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Farid Ammar-Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems. Mathematical Control and Related Fields, AIMS, 2017, 6 (2), pp.Pages: 185 - 216. 〈http://dx.doi.org/10.3934/mcrf.2016001〉. 〈hal-01115812v2〉

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