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Null controllability with constraints on the state for nonlinear heat equations
by
Massengo Mophou Gisèle
Université des Antilles et de la Guyane (Campus de fouillole) 97159 Pointe à Pitre, Guadeloupe (F.W.I)
Coauthors: Nakoulima Ousseynou
Université des Antilles et de la Guyane (Campus de fouillole) 97159 Pointe à Pitre, Guadeloupe (F.W.I)
We consider the null controllability problem with a finite number of constraints on the state for the semilinear heat equation in a bounded domain of \RN. The control is distributed along a bounded subset of the domain and the nonlinearity is assumed to be \C1 and globally Lipschitz. Interpreting each constraint by the notion of adjoint state, we transform the linearized problem into an equivalent null controllability problem with constraint on the control. Using a Carleman inequality adapted to the constraint, we prove first the null controllability of the linearized problem. Then, by a fixed-point method, we show that the same result holds when the nonlinearity is \C1 and globally Lipschitz.
Date received: January 22, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-82.