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

Abstract

Abstract 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 L2(Ω)×L2(Γ) and Lq(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 (L2(Ω) × L2(Γ), L2(q−1)(Ω) × L2(q−1)(Γ))-global attractor is obtained by asymptotical regularity method. Finally, we prove the existence of global attractor in W1,p(Ω) ∩ Lq(Ω)) × Lq(Γ) by asymptotic a priori estimate.