Boundary controllability for inhomogeneous multidimensional thermoelastic diffusion problem by Hilbert's uniqueness method

In this paper, we study the stabilization and the partial exact controllability of an inhomogeneous multidimensional thermoelastic diffusion problem by a memory function introduced on a part of the boundary of the material. By using the Nakao difference inequality, we prove that the energy of the system decays to zero exponentially at a rate determined explicitly by the physical parameters. Then by the Hilbert uniqueness method combined with Russell's principle “controllability via stabilizability” we prove that after certain threshold time moment the considered system is partially controllable under a smallness restriction on the coupling parameters stress-temperature and stress-diffusion. The boundary control function is determined explicitly.