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Partial null controllability of parabolic linear systems

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  • This paper is devoted to the partial null controllability issue of parabolic linear systems with $n$ equations. Given a bounded domain $\Omega$ in $\mathbb{R}^N$ ($N\in \mathbb{N}^*$), we study the effect of $m$ localized controls in a nonempty open subset $\omega$ only controlling $p$ components of the solution ($p,m \le n$). 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 $2\times2$ parabolic system, we will provide positive and negative results on partial null controllability when the coefficients are space dependent.
    Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 93C20, 93C05, 35K40.


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