Pullback attractors for a class of non-autonomous thermoelastic plate systems
| Autor: | Bezerra, Flank D. M., Carbone, Vera L., Nascimento, Marcelo J. D., Schiabel, Karina |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 21 pages. arXiv admin note: text overlap with arXiv:1012.4749 |
| Databáze: | arXiv |
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