Fixed point and best proximity theorems under two classes of integral-type contractive conditions in uniform metric spaces.
De La Sen, M. (2010)
Fixed Point Theory and Applications [electronic only]
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De La Sen, M. (2010)
Fixed Point Theory and Applications [electronic only]
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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...
Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form . We consider distributed controls with support in a small set and nonregular coefficients . For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.
Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.