Long-time asymptotics for a coupled thermoelastic plate-membrane system

TL;DR

This paper investigates the long-term behavior of a coupled thermoelastic plate-membrane system with various damping mechanisms, establishing well-posedness, regularity, and asymptotic stability depending on damping and rotational effects.

Contribution

It provides new results on the asymptotic behavior of coupled thermoelastic systems with different damping configurations and rotational inertia, extending previous analyses.

Findings

Proves well-posedness of the coupled system.

Establishes higher regularity of solutions.

Analyzes asymptotic stability depending on damping and rotational inertia.

Abstract

In this paper we consider a transmission problem for a system of a thermoelastic plate with (or without) rotational inertia term coupled with a membrane with different variants of damping for the plate and/or the membrane. We prove well-posedness of the problem and higher regularity of the solution and study the asymptotic behaviour of the solution, depending on the damping and on the presence of the rotational term.