Electron. J. Diff. Equ., Vol. 2015 (2015), No. 37, pp. 1-15.

Dynamics of the p-Laplacian equations with nonlinear dynamic boundary conditions

Xiyou Cheng, Lei Wei

Abstract:
In this article, we study the long-time behavior of the p-Laplacian equation with nonlinear dynamic boundary conditions for both autonomous and non-autonomous cases. For the autonomous case, some asymptotic regularity of solutions is proved. For the non-autonomous case, we obtain the existence and structure of a compact uniform attractor in $L^{r_1}(\Omega)\times L^{r}(\Gamma)$ ($r=\min(r_1,r_2)$).

Submitted May 6, 2014. Published February 10, 2015.
Math Subject Classifications: 37L05, 35B40, 35B41.
Key Words: p-Laplacian equation; boundary condition; asymptotic regularity; attractor.

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Xiyou Cheng
School of Mathematics and Statistics
Lanzhou University
Lanzhou 730000, China
email: chengxy@lzu.edu.cn
Lei Wei
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou 221116, China
email: wlxznu@163.com

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