On uniform attractors for non-autonomous \(p\)-Laplacian equation with dynamic boundary condition. (English) Zbl 1343.35144

Yang, Lu; Yang, Meihua; Wu, Jie

Topol. Methods Nonlinear Anal. 42, No. 1, 169-180 (2013).

Summary: 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.

MSC:

35K92	Quasilinear parabolic equations with \(p\)-Laplacian
35B41	Attractors
35B40	Asymptotic behavior of solutions to PDEs
37L05	General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations

Keywords:

parabolic equations; uniform attractors