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Article Dans Une Revue Electronic Journal of Qualitative Theory of Differential Equations Année : 2012

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

Résumé

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.

Dates et versions

hal-01679144 , version 1 (09-01-2018)

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Citer

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, 2012, 95, pp.1 - 34. ⟨10.14232/ejqtde.2012.1.95⟩. ⟨hal-01679144⟩

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