Exact-approximate boundary reachability of thermoelastic plates under variable thermal coupling
In this paper, we consider controllability properties of a thermoelastic plate equation, in which the (coupling) coefficient of thermal expansion α is allowed to vary with the properties of the plate. Boundary control is exerted through the free boundary conditions of the plate equation and through the Robin boundary condition of the temperature. These controls have the physical interpretation, respectively, of inserted forces/moments and prescribed temperature, all of which act on the edges of the plate. The main result here states that this boundary controlled partial differential equation has the following exact-approximate controllability property: with initial data of finite energy, one can find boundary controls such that the mechanical (plate) variable can be controlled exactly and the thermal variable approximately. The proof of this result relies on an inverse-type estimate which reconstructs the initial energy for the plate from measurements on the boundary.
Avalos, G., & Lasiecka, I. (2000). Exact-approximate boundary reachability of thermoelastic plates under variable thermal coupling. Inverse Problems, 16 (4), 979-996. https://doi.org/10.1088/0266-5611/16/4/307