Forced periodic solutions for piezoelectric crystals

The system of partial differential equations governing the dynamics and, in the stationary case, the electro-elastic equilibrium of a piezoelectric crystal when a given electric potential is applied on the surface, is studied in connection with the aspects of existence, uniqueness and regularity of solutions. We prove that the corresponding semigroup is in fact a group of isometries. When the data are periodic functions we also provide a condition for the existence of forced periodic vibrations in both the damped and undamped case.