Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms

V. R. Cabanillas, S. B. de Menezes and E. Zuazua

Journal of Optimization Theory and Applications, 2001, vol. 110, issue 2, No 1, 245-264

Abstract: Abstract We consider the null controllability problem for the semilinear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ℝ N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ω such that the uncontrolled region Ω\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.

Keywords: Null controllability; approximate controllability; unbounded domains; Carleman inequalities; observability inequality (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017515027783

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