A null controllability problem with a finite number of constraints on the normal derivative for the semilinear heat equation

Abstract : We consider the semilinear heat equation in a bounded domain of R^m. We prove the null controllability of the system with a finite number of constraints on the normal derivative, when the control acts on a bounded subset of the domain. First, we show that the problem can be transformed into a null controllability problem with constraint on the control, for a linear system. Then, we use an appropriate observability inequality to solve the linearized problem. Finally, we prove the main result by means of a fixed-point method.
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Contributor : Carole Louis-Rose <>
Submitted on : Tuesday, January 9, 2018 - 5:12:26 PM
Last modification on : Wednesday, July 18, 2018 - 8:11:27 PM

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Carole Louis-Rose. A null controllability problem with a finite number of constraints on the normal derivative for the semilinear heat equation. Electronic Journal of Qualitative Theory of Differential Equations, University of Szeged, Bolyai Institute, 2012, pp.1 - 34. ⟨10.14232/ejqtde.2012.1.95⟩. ⟨hal-01679144⟩

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