Controllability of the linear system of thermoelastic plates

Abstract

We prove that the linear system of thermoelastic plates, with finite speed of propagation of the elastic components, is controllable in the following sense: If the control time is large enough and we act in the equation of displacement by means of a control supported in a neighborhood of the boundary of the plate, then we may control exactly the displacement and simultaneously the temperature in an approximate way. The method of proof is an adaptation of the techniques developed by the second author for the proof of the exact-approximate controllability for the three-dimensional system of thermolelasticity and combines: (i) a decoupling result based on an idea due to Henry, Lopes and Perissinotto for three-dimensional thermoelasticity, (ii) the variational approach to controllability developed by Fabre, Puel and Zuazua and (iii) some observability inequalities for the system of thermoelastic plates.