Asymptotic behaviour of thermoviscoelastic Berger plate

TL;DR

This paper investigates the long-term behavior of a thermoviscoelastic Berger plate model, incorporating thermal effects, non-local nonlinearities, and memory effects, proving the existence of a compact global attractor.

Contribution

It introduces a novel analysis of the asymptotic behavior of a complex PDE system modeling thermoviscoelastic plates with memory effects, establishing the existence of a global attractor.

Findings

Existence of a compact global attractor for the system

Analysis of the asymptotic stability using stabilizability inequality

Characterization of the attractor's properties

Abstract

System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and fading memory of material is considered. The equation is transformed into a dynamical system in a suitable Hilbert space which asymptotic behaviour is analysed. Existence of the compact global attractor in this dynamical system and some of its properties are proved in this article. Main tool in analysis of asymptotic behaviour is stabilizability inequality.