Blow-up result for a piezoelectric beams system with magnetic effects

TL;DR

This paper investigates the conditions under which solutions to a piezoelectric beams system with magnetic effects blow up in finite time, highlighting the influence of damping and source term interactions.

Contribution

It introduces a blow-up analysis for a piezoelectric beams system with magnetic effects using the concavity method, focusing on negative initial energy scenarios.

Findings

Solutions blow up in finite time under certain conditions.

Damping and source term interactions are critical in blow-up behavior.

Negative initial energy leads to solution blow-up.

Abstract

The system under studying is for a piezoelectric beams system with magnetic effects, frictional dampings and source terms. We use the concavity method to study the competition of the dampings and the sources that leads to a blow-up result for solutions with negative initial energy.