Artículo
Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
Autor/es | Bodart, Olivier
González Burgos, Manuel Pérez García, Rosario |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2004 |
Fecha de depósito | 2016-05-23 |
Publicado en |
|
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, ... 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. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | PB98–1134 |
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. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Existence of insensitizing ... | 285.6Kb | [PDF] | Ver/ | |