### Correction to “Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity”

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In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical...

In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical...

The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to a related open question raised by Alabau and Komornik...

Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in ${L}^{2}\left(\Omega \right)\times {\left({H}^{1}\left(\Omega \right)\right)}^{\text{'}}$ and we derive estimates for the control time T.

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