NULL CONTROLLABILITY FOR THE SEMILINEAR HEAT EQUATION IN UNBOUNDED DOMAINS

Abstract

In this paper, we consider the null controllability problem for the semilinear heat equation in an unbounded domain of R N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain w such that the uncontrolled regian Ω w is bounded. Using Carleman inequalities we first prove the null controllabitity of the linearized equation. Then, by a fixed point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is globally Lipschitz, the system is null controllable.