[Contrôles insensibilisants pour une équation de la chaleur semi-linéaire avec non-linéarité superlinéaire]
Dans cette Note, on étudie l'existence de contrôles insensibilisants pour une équation de la chaleur semi-linéaire, avec des non-linéarités superlinéaires à l'infini. On démontre l'existence de contrôles insensibilisant la norme L2 de la solution observée dans un ouvert inclus dans le domaine considéré, sous des hypothèses convenables sur la non-linéarité et le second membre de l'équation. La démonstration fait appel à des inégalités de Carleman globales, la régularisation parabolique et un argument de point fixe.
This Note is concerned with the existence of insensitizing controls for a semilinear heat equation when we consider nonlinearities that behave superlinearly at infinity. We prove the existence of a control insensitizing the L2-norm of the observation of the solution in an open subset of the considered domain under appropriate assumptions on the nonlinear term f(y) and the second member ξ of the equation. The proof uses global Carleman estimates, parabolic regularity and a fixed point argument.
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@article{CRMATH_2002__335_8_677_0,
author = {Bodart, Olivier and Gonz\'alez-Burgos, Manuel and P\'erez-Garc{\'\i}a, Rosario},
title = {Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity},
journal = {Comptes Rendus. Math\'ematique},
pages = {677--682},
publisher = {Elsevier},
volume = {335},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02547-5},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02547-5/}
}
TY - JOUR AU - Bodart, Olivier AU - González-Burgos, Manuel AU - Pérez-García, Rosario TI - Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity JO - Comptes Rendus. Mathématique PY - 2002 SP - 677 EP - 682 VL - 335 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02547-5/ DO - 10.1016/S1631-073X(02)02547-5 LA - en ID - CRMATH_2002__335_8_677_0 ER -
%0 Journal Article %A Bodart, Olivier %A González-Burgos, Manuel %A Pérez-García, Rosario %T Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity %J Comptes Rendus. Mathématique %D 2002 %P 677-682 %V 335 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02547-5/ %R 10.1016/S1631-073X(02)02547-5 %G en %F CRMATH_2002__335_8_677_0
Bodart, Olivier; González-Burgos, Manuel; Pérez-García, Rosario. Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity. Comptes Rendus. Mathématique, Tome 335 (2002) no. 8, pp. 677-682. doi : 10.1016/S1631-073X(02)02547-5. http://www.numdam.org/articles/10.1016/S1631-073X(02)02547-5/
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