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On the controllability of parabolic systems with a nonlinear term involving the state and the gradient

 

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Opened Access On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
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Author: Doubova Krasotchenko, Anna
Fernández Cara, Enrique
González Burgos, Manuel
Zuazua Iriondo, Enrique
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2002
Published in: SIAM Journal on Control and Optimization, 41(2), 798-819
Document type: Article
Abstract: 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.
Size: 210.4Kb
Format: PDF

URI: http://hdl.handle.net/11441/41189

DOI: 10.1137/S0363012901386465

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