Sharp Estimates of the One-Dimensional Boundary Control Cost for Parabolic Systems and Application to the $N$-Dimensional Boundary Null Controllability in Cylindrical Domains
Abstract
In this paper we consider the boundary null controllability of a system of $n$ parabolic equations on domains of the form $\Omega =(0,\pi)\times \Omega_2$ with $\Omega_2$ a smooth domain of $\mathbb{R}^{N-1}$, $N>1$. When the control is exerted on $\{0\}\times \omega_2$ with $\omega_2\subset \Omega_2$, we obtain a necessary and sufficient condition that completely characterizes the null controllability. This result is obtained through the Lebeau--Robbiano strategy and requires an upper bound of the cost of the one-dimensional boundary null control on $(0,\pi)$. The latter is obtained using the moment method and it is shown to be bounded by $Ce^{C/T}$ when $T$ goes to $0^+$.
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Information & Authors
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Published In
SIAM Journal on Control and Optimization
Pages: 2970 - 3001
DOI: 10.1137/130929680
ISSN (online): 1095-7138
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© 2014, Society for Industrial and Applied Mathematics.
History
Submitted: 18 July 2013
Accepted: 9 July 2014
Published online: 25 September 2014
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