Regularity and fractal dimension of pullback attractors for a non-autonomous semilinear degenerate parabolic equation

摘要

Considered here is the pullback attractor of the process associated with the first initial boundary value problem for the non-autonomous semilinear degenerate parabolic equation u_t - div(σ(x)?u)+f(u) = g(x,t) in a bounded domain Ω in ?~N (N≥2). We prove the regularity in the space L ~(2p-2)(Ω)∩ D-~2 _0(Ω,σ), and estimate the fractal dimension of the pullback attractor in L ~2(Ω).