1. Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains
- Author
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Franck Boyer, Guillaume Olive, Manuel González-Burgos, Assia Benabdallah, Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Ministerio de Ciencia e Innovación (MICIN). España, Laboratoire d'Analyse, Topologie, Probabilités (LATP), Université Paul Cézanne - Aix-Marseille 3-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS), Dpto,~E.D.A.N., Universidad de Sevilla, analyse appliquée, and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
0209 industrial biotechnology ,Pure mathematics ,Control and Optimization ,Boundary Controllability ,Mathematics::General Topology ,Boundary (topology) ,parabolic systems ,02 engineering and technology ,93B05, 93C05, 35K05 ,01 natural sciences ,Upper and lower bounds ,Omega ,Domain (mathematical analysis) ,Kalman rank condition ,020901 industrial engineering & automation ,Parabolic systems ,0101 mathematics ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Null (mathematics) ,Mathematical analysis ,boundary controllability ,Kalman Rank condition ,Parabolic partial differential equation ,Controllability ,Mathematics::Logic ,biorthogonal families ,Bounded function ,Biorthogonal families ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] - Abstract
International audience; 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 $\R^{N-1}$, $N>1$. 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 require an upper bound of the cost of the one-dimensional boundary null-control on $(0,\pi)$. This latter is obtained using the moment method and it is shown to be bounded by $Ce^{C/T}$ when $T$ goes to $0^+$.
- Published
- 2014
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