Dynamics for a class of non-autonomous degenerate p-Laplacian equations

In this paper, we investigate a class of non-autonomous degenerate p-Laplacian equations∂tu−div(a(x)|∇u|p−2∇u)+λu+f(u)=g(x,t) in Ω, where a(x) is allowed to vanish on a nonempty closed subset with Lebesgue measure zero, g(x,t)∈Llocp′(R;D−1,p′(Ω,a)) and Ω an unbounded domain in RN. We first establish the well-posedness of these equations by constructing a compact embedding. Then we show the existence of the minimal pullback Dμ-attractor, and prove that it indeed attracts the Dμ class in L2+δ-norm for any δ∈[0,∞). Our results extend some known ones in previously published papers.