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 $$\{\begin{array}{ll}{u}_{tt}+\eta {\Delta }^{2}u+a(t)\Delta \theta =f(t,u),& t>\tau ,x\in \Omega ,\\ {\theta }_t-\kappa \Delta \theta -a(t)\Delta u_t=0,& t>\tau ,x\in \Omega ,\end{array}$$ 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 $N⩾2$, which boundary $\partial \Omega$ is assumed to be a ${\mathcal{C}}^4$-hypersurface, $\eta >0$ and $\kappa >0$ are constants, $a$ is an Hölder continuous function, $f$ is a dissipative nonlinearity locally Lipschitz in the second variable.

21 pages. arXiv admin note: text overlap with arXiv:1012.4749