Time-dependent attractors for non-autonomous non-local reaction–diffusion equations. Issue 5 (22nd April 2018)

• Record Type: Journal Article
• Authors: Caraballo, Tomás; Herrera-Cobos, Marta; Marín-Rubio, Pedro
• Is Part Of: Proceedings. Volume 148:Issue 5(2018)
• Page Start: 957
• Page End: 981
• Publication Date: 2018-04-22
• Subjects: non-autonomous non-local reaction–diffusion equations, -- pullback attractors, -- asymptotic compactness, -- regularity of attractors; 35B41, -- 35B65, -- 35K57, -- 35Q92, -- 37L30; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210517000348
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : 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.