The cost of approximate controllability for semilinear heat equations

摘要

We consider the semilinear heat equation withglobally Lipschitz non-linearity involving gradient terms in a bounded domain of Rn. In this paper, we obtain explicit bounds of the cost of approximate controllability, i.e., of the minimal norm of a control needed to control the system approximately. The methods we used combine global Carleman estimates, the variational approach to approximate controllability and Schauder's fixed point theorem.