On the cost of fast controls for thermoelastic plates

This paper proves that any initial condition in the energy space for the system of thermoelastic plates without rotatory inertia on a smooth bounded domain with hinged mechanical boundary conditions and Dirichlet thermal boundary condition can be steered to zero by a square integrable input function, either mechanical or thermal, supported in arbitrarily small sub-domain and time interval [0,T]. As T tends to zero, for initial states with unit energy norm, the norm of this input function grows at most like exp (C_p/T^p) for any real p>1 and some C_p>0. These results are analogous to the optimal ones known for the heat flow and the proof uses the heat control strategy of Lebeau and Robbiano.