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

• Main Authors: Xiyou Cheng, Lei Wei
• Format: Article
• Language: English
• Published: Texas State University 2015-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: p-Laplacian equation; boundary condition; asymptotic regularity; attractor
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/37/abstr.html
• ISSN: 1072-6691

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 $L^{r_1}(\Omega)\times L^{r}(\Gamma)$ ($r=\min(r_1,r_2)$).