Article
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
Author/s | Fernández Cara, Enrique
González Burgos, Manuel Guerrero Rodríguez, Sergio Puel, Jean-Pierre |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2006-07 |
Deposit Date | 2016-05-20 |
Published in |
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Abstract | 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 ∂y ∂n + f(y) = 0. We ... 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 ∂y ∂n + f(y) = 0. 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, one has exact controllability to the trajectories. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | BFM2000–1317
BFM2003–06446 |
Citation | Fernández Cara, E., González Burgos, M., Guerrero, S. y Puel, J. (2006). Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case. ESAIM: Control, Optimisation and Calculus of Variations, 12 (3), 466-483. |
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