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 ${ℝ}^n$ 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 ${\left[L^2\left({ℝ}^n\right)\right]}^3$ and ${\left[H^1\left({ℝ}^n\right)\right]}^3$, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.