Pullback attractors for non-autonomous reaction-diffusion equations on ℝ n .

We study the long time behavior of solutions of the non-autonomous reaction-diffusion equation defined on the entire space ℝ n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L 2(ℝ n ) and H 1(ℝ n ), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains. [ABSTRACT FROM AUTHOR]