Pullback 𝒟-Attractor of Nonautonomous Three-Component Reversible Gray-Scott System on Unbounded Domains

Abstract

The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire space ℝn is studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L2ℝn3 and H1ℝn3, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.