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...
| Autores: | , , , |
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| 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 |
| 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+. |
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