Automatic feedback control for one class of contact piezoelectric problems - Zgurovsky, M.Z.; Kasyanov, P.O.; Paliichuk, L.S. (Системні дослідження та інформаційні технології, 2014)
In this paper we investigate the dynamics of solutions of the second order evolution inclusion with discontinuous interaction function which can be represented as the difference of subdifferentials. This case is actual for feedback automatic control problems. In particular, we concider mathematical model of contact piezoelectric process between a piezoelectric body and a foundation and for this problem investigate the long-term behavior of state function. We deduce a priory estimates for weak solutions of studied problem in the phase spase. The theorem on the existence of a global attractor for multi-valued semiflow generated by weak solutions of the problem and the structural properties of the limit sets is prooved. The main results of the paper were applied to the investigated piezoelectric problem.