Null Controllability of a Thermoelastic Plate

In this paper, we investigate the null controllability of thermoelastic plates when the control (heat source) acts in the thermal equation. In general, these models consist of an elastic motion equation and a heat equation, which are coupled in such a way that the energy transfer between them is taken into account. The plate, we consider here, is derived in the light of [18]. Transverse shear effects are neglected (Euler-Bernoulli model), and the plate is hinged on its edge. In addition to internal and external heat source, the temperature dynamics are driven by internal frictional forces caused by the motion of the plate. The latter connection is expressed by the second law of thermodynamics for irreversible processes, which relates the entropy to the elastic strains. Accounting for thermal effects, we assume that the heat flux law involves only the temperature gradient by the Fourier law. Let Ω be a bounded, open, connected subset of R2, with a C∞ boundary and ω any open subset of Ω. Let T > 0 and set