Time-dependent attractors for non-autonomous non-local reaction–diffusion equations

In this paper the existence and uniqueness of weak and strong solutions for a non-autonomous non-local reaction–diffusion equation is proved. Furthermore, the existence of minimal pullback attractors in the L 2 -norm in the frameworks of universes of fixed bounded sets and those given by a tempered growth condition is established, along with some relationships between them. Finally, we prove the existence of minimal pullback attractors in the H 1 -norm and study relationships among these new families and those given previously in the L 2 context. We also present new results in the autonomous framework that ensure the existence of global compact attractors as a particular case.