Partial exact controllability and exponential stability in higher-dimensional linearthermoelasticity

Abstract

The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity isconsidered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, toincrease the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer toa related open question raised by Alabau and Komornik for the Lamé system. Via Russell's “Controllability via Stabilizability" principle, we thenprove that the thermoelastic system is partially controllable with boundary controls without smallness restrictions on the coupling parameters.