Attractors in $H^2$ and $L^{2p-2}$ for reaction diffusion equations on unbounded domains

We are concerned with a class of reaction diffusion equations with nonlinear terms of arbitrary growth on unbounded domains. The existence of an $L^2 - L^{2p-2} \cap H^2$ global attractor is proved. This improves the results in previous references, and the proof is shorter.