Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls
Alexander Khapalov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexander Khapalov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Anna Doubova, A. Osses, J.-P. Puel (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where...
T. Horsin (1998)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexander Y. Khapalov (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability...
S. Guerrero, O. Yu. Imanuvilov (2007)
Annales de l'I.H.P. Analyse non linéaire
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Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear,...