Boundary Controllability of Thermoelastic Plates via the Free Boundary Conditions

Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free boundary conditions of the plate equation and through the Robin boundary condition of the temperature. These controls have the physical interpretation of inserted forces and moments and prescribed temperature, respectively, all of which act on the edges of the plate. The main result here is that under such boundary control, and with initial data in the basic space of well-posedness, one can simultaneously control the displacement of the plate exactly and the temperature approximately. Moreover, the thermal control may be taken to be arbitrarily smooth in time and space, and the thermal control region may be any nonempty subset of the boundary. This controllability holds for arbitrary values of the coupling parameter α, with the optimal controllability time in line with that seen for uncoupled Kirchoff plates.