Carlos Castro (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.
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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Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.
V. Komornik (1989)
Annales de l'I.H.P. Analyse non linéaire
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Luz de Teresa (1998)
Revista Matemática Complutense
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The exact internal controllability of the radial solutions of a semilinear heat equation in R is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.
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...
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...