Exact distributed controllability for the semilinear wave equation.
Liu, Wei-Jiu (2000)
Portugaliae Mathematica
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Liu, Wei-Jiu (2000)
Portugaliae Mathematica
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E. Zuazua (1993)
Annales de l'I.H.P. Analyse non linéaire
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M. Asch, G. Lebeau (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the wave equation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry of the controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and an energetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical...
Brice Allibert (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We analyze the controllability of the wave equation on a cylinder when the control acts on the boundary, that does not satisfy the classical geometric control condition. We obtain precise estimates on the analyticity of reachable functions. As the control time increases, the degree of analyticity that is required for a function to be reachable decreases as an inverse power of time. We conclude that any analytic function can be reached if that control time is large enough. In the...
Sergei Avdonin, Victor Mikhaylov (2008)
Applicationes Mathematicae
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We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the...
Nicolae Cîndea, Enrique Fernández-Cara, Arnaud Münch (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not apply in this work the usual duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible...
Karine Beauchard (2005-2006)
Séminaire Équations aux dérivées partielles
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One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite...