Global existence and long time behavior of solutions to a model of ferroelectric materials

In this work we study a general model arising in the dynamic of ferroelectric materials with displacement. The storage energy contains several terms allowing to take into account the actions of the polarization field and the strain tensor. We prove, by using regularization and compactness methods (see [5]), existence of global in time weak solutions with finite energy. We also study the quasi-stationary model as well as the steady state model for which we establish existence of solutions. Finally we deal with the long time behavior of solutions of the quasi-static problem and show that as the time goes to infinity these solutions stabilize sequentially to a solution of the stationary problem.