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

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    * Corresponding author

The first author is partially supported by FAPESP grant #2014/03686-3, Brazil.
The third author is partially supported by FAPESP grant #2014/03109-6, Brazil.

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  • In this article we study the asymptotic behavior of solutions, in the sense of pullback attractors, of the evolution system

    $\begin{cases}u_{tt} +Δ^2 u+a(t)Δθ=f(t,u),&t>τ,\ x∈Ω,\\θ_t-κΔ θ-a(t)Δ u_t=0,&t>τ,\ x∈Ω,\end{cases}$

    subject to boundary conditions

    $u=Δ u=θ=0,\ t>τ,\ x∈\partial Ω,$

    where $Ω$ is a bounded domain in $\mathbb{R}^N$ with $N≥ 2$, which boundary $\partialΩ$ is assumed to be a $\mathcal{C}^4$-hypersurface, $κ>0$ is constant, $a$ is an Hölder continuous function and $f$ is a dissipative nonlinearity locally Lipschitz in the second variable. Using the theory of uniform sectorial operators, in the sense of P. Sobolevskiǐ ([23]), we give a partial description of the fractional power spaces scale for the thermoelastic plate operator and we show the local and global well-posedness of this non-autonomous problem. Furthermore we prove existence and uniform boundedness of pullback attractors.

    Mathematics Subject Classification: Primary: 37B55, 34D45; Secondary: 35B40, 35B41.


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