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Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity

Opened Access Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity

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Autor: Bodart, Olivier
González Burgos, Manuel
Pérez García, Rosario
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2004
Publicado en: Communications in Partial Differential Equations, 29 (7-8), 1017-1050.
Tipo de documento: Artículo
Resumen: In this paper we consider a semilinear heat equation (in a bounded domain Ω of IRN ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L2−norm of the observation of the solution in another open subset O ⊂ Ω when ω ∩ O 6= ∅, under suitable assumptions on the nonlinear term f(y) and the right hand side term ξ of the equation. The proof, involving global Carleman estimates and regularizing properties of the heat equation, relies on the sharp study of a similar linearized problem and an appropriate fixed-point argument. For certain superlinear nonlinearities, we also prove an insensitivity result of a negative nature. The crucial point in this paper is the technique of construction of L r–controls (r large enough) starting from insensitizing controls in L 2.
Cita: Bodart, O., González Burgos, M. y Pérez García, R. (2004). Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity. Communications in Partial Differential Equations, 29 (7-8), 1017-1050.
Tamaño: 285.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41481

DOI: http://dx.doi.org/10.1081/PDE-200033749

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