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A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions

Opened Access A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions

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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: SIAM Journal on Control and Optimization, 43 (3), 955-969.
Tipo de documento: Artículo
Resumen: 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.
Cita: Bodart, O., González Burgos, M. y Pérez García, R. (2004). A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions. SIAM Journal on Control and Optimization, 43 (3), 955-969.
Tamaño: 188.0Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41470

DOI: 10.1137/S036301290343161X

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