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

Abstract

We study the long time behavior of solutions of the non-autonomous reaction-diffusion equation defined on the entire space ℝn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L2(ℝn) and H1(ℝn), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.