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Título:
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On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient
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Autores:
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Doubova, Anna ;
Fernández Cara, E. ;
González Burgos, Manuel ;
Zuazua Iriondo, Enrique
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Tipo de documento:
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texto impreso
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Editorial:
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Siam Publications, 2002
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis numérico
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Tipo = Artículo
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Resumen:
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We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\mathbb R}^N$ 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 $f( y, \nabla y)$ grows slower than $|y| \log^{3/2}(1+ |y| + |\nabla y|) + |\nabla y| \log^{1/2}(1+ |y| + |\nabla y|)$ 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.
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En línea:
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https://eprints.ucm.es/id/eprint/12178/1/2001onthecon-19.pdf
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