Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41481 |
| Acceso en línea: | http://hdl.handle.net/11441/41481 https://doi.org/10.1081/PDE-200033749 |
| Access Level: | acceso abierto |
| Sumario: | 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. |
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