Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials

Using the asymptotic a priori estimate method, we prove the existence of a pullback D-attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of R-N (N >= 3), with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback D-attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.