Uniform attractor of a non-autonomous Lame thermoelastic system

TL;DR

This paper studies the long-term behavior of non-autonomous Lame thermoelastic systems in N-dimensional materials, proving the existence of a uniform attractor under certain conditions.

Contribution

It establishes the existence of a uniform attractor for the system using Lyapunov functions and contraction mapping, under specific nonlinear and irrotational conditions.

Findings

Existence of a uniformly absorbing set

Uniformly asymptotic compactness of the system

Existence of a uniform attractor in space H_c

Abstract

In this paper, we investigate the dynamical behavior of non-autonomous Lame thermoelastic systems within $N$-dimensional materials. With appropriate constraints on nonlinear characteristics and functional parameters, we initially establish the existence of a uniformly absorbing set by constructing a Lyapunov function. Subsequently, we employ the contraction mapping principle to demonstrate the uniformly asymptotic compactness of the system. Finally, under irrotational conditions, we prove the existence of a uniform attractor $\mathcal{A}_\Sigma$ in the space $H_c$.