# American Institute of Mathematical Sciences

March  2018, 7(1): 1-31. doi: 10.3934/eect.2018001

## The controllability of a thermoelastic plate problem revisited

 1 Université de Carthage, UR Systèmes dynamiques et applications, UR 17ES21, Ecole Nationale d'Ingénieurs de Bizerte, 7035, BP 66, Tunisia 2 Université de Carthage, UR Systèmes dynamiques et applications, UR 17ES21, Faculté des Sciences de Bizerte, Jarzouna 7021, Tunisia

Received  November 2016 Revised  November 2017 Published  January 2018

In this paper, the controllability for a thermoelastic plate problem with a rotational inertia parameter is considered under two scenarios. In the first case, we prove the exact and approximate controllability when the controls act in the whole domain. In the second case, we prove the interior approximate controllability when the controls act only on a subset of the domain. The distributed controls are determined explicitly by the physical constants of the plate in the first case, while this is no longer possible in the second case as the relation (79) is no longer valid. In this case, we propose an approximation of the control function with an error that tends to zero. By means of a powerful and systematic approach based on spectral analysis, we improve some already existing results on the optimal rate of the exponential decay and on the analyticity of the associated semigroup.

Citation: Moncef Aouadi, Taoufik Moulahi. The controllability of a thermoelastic plate problem revisited. Evolution Equations & Control Theory, 2018, 7 (1) : 1-31. doi: 10.3934/eect.2018001
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##### References:
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