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
\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).