Abstract
We consider the null controllability problem for the semilinear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ? N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ? such that the uncontrolled region Ω\? is bounded. Using Carleman inequalities, we prove first the null controllability 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 C1 and globally Lipschitz, the system is null controllable.
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