A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41470 |
| Acesso em linha: | http://hdl.handle.net/11441/41470 https://doi.org/10.1137/S036301290343161X |
| Access Level: | acceso abierto |
| Palavra-chave: | controllability nonlinear PDE of parabolic type |
| Resumo: | In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result. The boundary conditions we are dealing with lead us to seek a fixed point, and thus also control functions, in certain H¨older spaces. The main strategy in this paper is the construction of controls with H¨olderian regularity starting from L2-controls in the linear case. Sufficient regularity in the data and appropriate assumptions on the right-hand side term ξ of the equation are required. |
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