A note on the IBVP for wave equations with dynamic boundary conditions

The systemmodels an elastic body’s transverse vibration. For details, please see the paper of Lemrabet []. In [–] and the references therein, one can find more details as regards dynamic boundary conditions. Moreover, Heminna [] gives the controllability for elasticity system with two controls: both tangential and normal, under the assumption of the wellposedness for the backward system, which is a key assumption for getting controllability. In this paper, we establish first of all the wellposedness theorem for back-ward systems based on the transposition method (cf. []) and then obtain the controllability on the IBVP for the wave equation above by using the method of HUM.