Long-time dynamics for a piezoelectric system with time-varying delay and memory

Abstract

In this paper, we study the long time dynamics of piezoelectric system with damping term, past history and time-varying delay effects. We prove the well-posedness of the solution by the semigroup theory. Then the existence of global attractors with finite fractal dimension and the existence of exponential attractors are proved. Moreover, the upper semicontinuity of the global attractor is shown. Finally, the fact that the total energy of the system decays exponentially under suitable conditions is also derived.