Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions

Lu Yang; Meihua Yang; Peter E. Kloeden

doi:10.3934/dcdsb.2012.17.2635

Article Contents

2012, Volume 17, Issue 7: 2635-2651. Doi: 10.3934/dcdsb.2012.17.2635

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Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074
3.
Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main

Received: April 2012

Revised: May 2012

Published: October 2012

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Abstract

The existence of a unique minimal pullback attractor is established for the evolutionary process associated with a non-autonomous quasi-linear parabolic equations with a dynamical boundary condition in $L^{r_1}(\Omega)\times L^{r_1}(\Gamma)$ under that assumption that the external forcing term satisfies a weak integrability condition, where $r_1$ $>$ $2$ is determined by the order of the nonlinearity.

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Mathematics Subject Classification: 37L05, 35B40, 35B41.

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