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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V. Komornik (1989)
Annales de l'I.H.P. Analyse non linéaire
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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.
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.
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...
Enrique Fernández-Cara, Enrique Zuazua (2000)
Annales de l'I.H.P. Analyse non linéaire
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S. Guerrero, O. Yu. Imanuvilov (2007)
Annales de l'I.H.P. Analyse non linéaire
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