On the cost of fast controls for thermoelastic plates

Article type: Research Article

Authors: Miller, Luc

Affiliations: CMLS, École Polytechnique, 91128 Palaiseau cedex, France E-mail: [email protected]

Abstract: 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 (Cp/Tp) for any real p>1 and some Cp>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.

Keywords: controllability, thermoelasticity, plates

Journal: Asymptotic Analysis, vol. 51, no. 2, pp. 93-100, 2007