Pullback attractors for a class of non-autonomous thermoelastic plate systems

TL;DR

This paper investigates the long-term behavior of solutions to a non-autonomous thermoelastic plate system, establishing the existence of global pullback attractors under certain conditions.

Contribution

It introduces a framework for analyzing pullback attractors for a class of non-autonomous thermoelastic systems with specific boundary conditions.

Findings

Existence of global pullback attractors proven.

Asymptotic behavior characterized for the system.

Conditions on nonlinearity and coefficients established.

Abstract

In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ \begin{cases} u_{tt} +\eta\Delta^2 u+a(t)\Delta\theta=f(t,u), & t>\tau,\ x\in\Omega,\\ \theta_t-\kappa\Delta \theta-a(t)\Delta u_t=0, & t>\tau,\ x\in\Omega, \end{cases} $$ subject to boundary conditions $$ u=\Delta u=\theta=0,\ t>\tau,\ x\in\partial\Omega, $$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\Omega$ is assumed to be a $\mathcal{C}^4$-hypersurface, $\eta>0$ and $\kappa>0$ are constants, $a$ is an H\"older continuous function, $f$ is a dissipative nonlinearity locally Lipschitz in the second variable.