Exact-approximate boundary reachability of thermoelastic plates under variable thermal coupling

in this paper, we consider controllability properties of a thermoelastic pl ate equation, in which the (coupling) coefficient of thermal expansion alph a is allowed to vary with the properties of the plate. Boundary control is exerted through the for boundary conditions of the plate equation and throu gh the Robin boundary condition of the temperature. These controls have the physical interpretation, respectively, of inserted forces/moments and pres cribed temperature, all of which act on the edges of the plate. The main re sult here states that this boundary controlled partial differential equatio n has the following exact-approximate controllability property: with initia l data of finite energy, one can find boundary controls such that the mecha nical (plate) variable can be controlled exactly and the thermal variable a pproximately. The proof of this result relies on an inverse-type estimate w hich reconstructs the initial energy for the plate from measurements on the boundary.