Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings

TL;DR

This paper studies the long-term behavior of a piezoelectric system with magnetic effects, nonlinear damping, and external forces, establishing well-posedness, attractor properties, and stability under parameter variations.

Contribution

It introduces a comprehensive analysis of the system’s long-time dynamics, including well-posedness, global and exponential attractors, and their upper semicontinuity, which is novel for this model.

Findings

Proved well-posedness of solutions using nonlinear semigroup theory.

Established existence of global and exponential attractors.

Demonstrated upper semicontinuity of global attractors.

Abstract

This paper is concerned with the long-time dynamical behavior of a piezoelectric system with magnetic effect, which has nonlinear damping terms and external forces with a parameter. At first, we use the nonlinear semigroup theory to prove the well-posedness of solutions. Then, we investigate the properties of global attractors and the existence of exponential attractors. Finally, the upper semicontinuity of global attractors has been investigated.