Stability analysis for a plate-membrane system without geometric condition

TL;DR

This paper investigates the stability of a thermoelastic plate-membrane system, demonstrating the absence of exponential stability and establishing polynomial stability without relying on typical geometric conditions.

Contribution

It provides the first analysis showing polynomial stability for this system without the standard geometric assumptions.

Findings

No exponential stability for the system.

Polynomial stability is achieved without geometric conditions.

Results extend understanding of thermoelastic systems' stability.

Abstract

In this work, we consider a transmission problem describing a thermoelastic plate surrounding a membrane without any mechanical damping. The main results consist of the lack of exponential stability for this problem and the polynomial stability without the usual geometric condition.