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

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.