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This paper studies the long-time behavior of solutions for p-Laplacian equations with a polynomial growth nonlinearity of arbitrary order and dynamic flux boundary conditions in d-dimensional bounded smooth domains. We first prove the existence of global attractors in L 2 (Ω)×L 2 (Γ) and L q (Ω)×Lq(Γ) for the p-Laplacian evolution equations subject to dynamic nonlinear boundary conditions by using the Sobolev compactness embedding theory, and then the existence of (L 2 (Ω) × L 2 (Γ), L 2(q−1) (Ω) × L 2(q−1) (Γ))-global attractor is obtained by asymptotical regularity method. Finally, we prove the existence of global attractor in W 1,p (Ω) ∩ L q (Ω)) × L q (Γ) by asymptotic a priori estimate.

Global Attractors for p-Laplacian Equations with Dynamic Flux Boundary Conditions