REGULARITY AND FRACTAL DIMENSION OF PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMILINEAR DEGENERATE PARABOLIC EQUATION

Abstract

AbstractConsidered here is the pullback attractor of the process associated with the first initial boundary value problem for the non-autonomous semilinear degenerate parabolic equation \begin{linenomath} u_t-\text{div}(\sigma(x)\nabla u)+f(u)=g(x,t) \end{linenomath} in a bounded domain Ω in ℝN (N≥2). We prove the regularity in the space L2p−2(Ω)∩ $D_0^2(\Omega,\sigma)$, and estimate the fractal dimension of the pullback attractor in L2(Ω).