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

V. R. Cabanillas, S. B. De Menezes, E. Zuazua

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39 Citas (Scopus)

Resumen

We consider the null controllability problem for the semi-linear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ℝN 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.

Idioma originalInglés
Páginas (desde-hasta)245-264
Número de páginas20
PublicaciónJournal of Optimization Theory and Applications
Volumen110
N.º2
DOI
EstadoPublicada - ago. 2001
Publicado de forma externa

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