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

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 char...

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Detalles Bibliográficos
Autores: Benabdallah, Assia, Boyer, Franck, González Burgos, Manuel, Olive, Guillaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41457
Acceso en línea:http://hdl.handle.net/11441/41457
https://doi.org/10.1137/130929680
Access Level:acceso abierto
Palabra clave:parabolic systems
boundary controllability
biorthogonal families
Kalman rank condition
Descripción
Sumario: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+.