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 ∂ t u − div ( a ( x ) | ∇ u | p − 2 ∇ u ) + λ u + 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 ) ∈ L l o c p ′ ( R ; D − 1 , p ′ ( Ω , a ) ) and Ω an unbounded domain in R N . We first establish the well-posedness of these equations by constructing a compact embedding. Then we show the existence of the minimal pullback D μ -attractor, and prove that it indeed attracts the D μ class in L 2 + δ -norm for any δ ∈ [ 0 , ∞ ) . Our results extend some known ones in previously published papers. [ABSTRACT FROM AUTHOR]