Pullback attractors for non-autonomous reaction-diffusion equations on ℝⁿ

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.

Keywords

Pullback attractor / asymptotic compactness / non-autonomous equation

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