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Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains

 

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Opened Access Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains
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Author: Benabdallah, Assia
Boyer, Franck
González Burgos, Manuel
Olive, Guillaume
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2014
Published in: SIAM Journal on Control and Optimization, 52 (5), 2970-3001.
Document type: Article
Abstract: In this paper we consider the boundary null controllability of a system of n parabolic equations on domains of the form Ω = (0, π) × Ω2 with Ω2 a smooth domain of RN−1, N > 1. When the control is exerted on {0} × ω2 with ω2 ⊂ Ω2, 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, π). The latter is obtained using the moment method and it is shown to be bounded by CeC/T when T goes to 0+.
Cite: Benabdallah, A., Boyer, F., González Burgos, M. y Olive, G. (2014). Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains. SIAM Journal on Control and Optimization, 52 (5), 2970-3001.
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URI: http://hdl.handle.net/11441/41457

DOI: http://dx.doi.org/10.1137/130929680

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