Piezoelectric beam with magnetic effect, time-varying delay and time-varying weights

TL;DR

This paper studies a piezoelectric beam model with magnetic effects, time-varying delays, and weights, proving exponential decay of solutions and addressing existence and uniqueness.

Contribution

It introduces a novel model incorporating magnetic effects and time-varying delays, and establishes exponential decay and well-posedness results.

Findings

Solutions decay exponentially over time.

Existence and uniqueness of solutions are proven.

Damping effects with time-varying weights are effective.

Abstract

The main result of this work is to obtain the exponential decay of the solutions of a piezoelectric beam model with magnetic effect and delay term. The dampings are inserted into the equation of longitudinal displacement. The terms of damping, whose weight associated with them varies over time, are of the friction type, and one of them has delay. This work will also address the issue of existence and uniqueness of solution for the model.