Artículo
On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
Autor/es | Doubova Krasotchenko, Anna
Fernández Cara, Enrique González Burgos, Manuel Zuazua Iriondo, Enrique |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2002 |
Fecha de depósito | 2016-05-13 |
Publicado en |
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Resumen | We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem ... We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term f(y, ∇y) grows slower than |y| log3/2(1+ |y|+ |∇y|)+ |∇y| log1/2(1+ |y|+ |∇y|) at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | PB96-0663
PB98-1134 BFM2000-1317 |
Cita | Doubova Krasotchenko, A., Fernández Cara, E., González Burgos, M. y Zuazua Iriondo, E. (2002). On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. |
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