Null controllability in unbounded domains for the semilinear heat equationwith nonlinearities involving gradient terms

We consider the null controllability problem for the semilinear heat equati on with nonlinearities involving gradient terms in an unbounded domain Omeg a of R-N with Dirichlet boundary conditions. The control is assumed to be d istributed along a subdomain omega such that the uncontrolled region Omega\ omega is bounded. Using Carleman inequalities, we prove first. the null con trollability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, w hen the nonlinearity is C-1 and globally Lipschitz, the system is null cont rollable.