On uniform attractors for non-autonomous $p$-Laplacian equation with a dynamic boundary condition

Abstract

In this paper, we consider the non-autonomous $p$-Laplacian equation with a dynamic boundary condition. The existence and structure of a compact uniform attractor in $W^{1,p}(\Omega)\times W^{1-1/p,p}(\Gamma)$ are established for the case of time-dependent internal force $h(t)$. While the nonlinearity $f$ and the boundary nonlinearity $g$ are dissipative for large values without restriction on the growth order of the polynomial.