Artículo
On the controllability of the heat equation with nonlinear boundary Fourier conditions
Autor/es | Doubova Krasotchenko, Anna
Fernández Cara, Enrique González Burgos, Manuel |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2004-01-20 |
Fecha de depósito | 2016-05-23 |
Publicado en |
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Resumen | In this paper we analyze the approximate and null controllability of the classical heat equation with nonlinear boundary conditions of the form
∂y ∂n + f(y) = 0 and distributed controls, with support in a small set. We ... In this paper we analyze the approximate and null controllability of the classical heat equation with nonlinear boundary conditions of the form ∂y ∂n + f(y) = 0 and distributed controls, with support in a small set. We show that, when the function f is globally Lipschitz-continuous, the system is approximately controllable. We also show that the system is locally null controllable and null controllable for large time when f is regular enough and f(0) = 0. For the proofs of these assertions, we use controllability results for similar linear problems and appropriate fixed point arguments. In the case of the local and large time null controllability results, the arguments are rather technical, since they need (among other things) Hölder estimates for the control and the state. |
Agencias financiadoras | Ministerio de Ciencia y Tecnología (MCYT). España |
Identificador del proyecto | PB98–1134
BFM2000–1317 |
Cita | Doubova Krasotchenko, A., Fernández Cara, E. y González Burgos, M. (2004). On the controllability of the heat equation with nonlinear boundary Fourier conditions. Journal of Differential Equations, 196 (2), 385-417. |
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