Polynomial energy decay rate of a 2D Piezoelectric beam with magnetic effect on a rectangular domain without geometric conditions

TL;DR

This paper proves that the energy of a 2D piezoelectric beam with magnetic effects on a rectangular domain decays at a polynomial rate of 1/t, even with minimal damping and no geometric restrictions.

Contribution

It establishes the polynomial decay rate for a coupled piezoelectric-magnetic system without geometric conditions and with limited damping.

Findings

Energy decays at rate 1/t

Polynomial stability established for the system

No geometric conditions needed for decay

Abstract

In this paper, we investigate the stability of coupled equations modelling a 2D piezoelectric beam with magnetic effect with only one local viscous damping on a rectangular domain without geometric conditions. We prove that the energy of the system decays polynomially with the rate 1/t .