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Issue ESAIM: COCV
Volume 2, 1997
Page(s) 87 - 103
DOI 10.1051/cocv:1997104

ESAIM: COCV, Vol. 2, pp. 87-103
DOI: 10.1051/cocv:1997104

Null controllability of the semilinear heat equation

E. Fernandez-Cara


Abstract
This paper is concerned with the null controllability of systems governed by semilinear parabolic equations. The control is exerted either on a small subdomain or on a portion of the boundary. We prove that the system is null controllable when the nonlinear term f(s) grows slower than s . log|s| as |s| tends to infinity.


Résumé
Ce papier est consacré à l'étude de la contrôlabilité nulle des systèmes gouvernés par des équations aux dérivées partielles paraboliques semilinéaires. Le contrôle est localisé dans un (petit) sous-domaine ou sur une (petite) partie de la frontière. Les résultats principaux montrent que le système est exactement contrôlable à zéro si le terme non linéaire f(s) croît plus lentement que s . log|s| quand |s| tend vers l'infini.


Key words: Null controllability / semilinear parabolic partial differential equations / fixed-point method.


© EDP Sciences, SMAI 1997


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