Asymptotic behavior for a class of nonlocal nonautonomous problems

Asymptotic behavior for a class of nonlocal nonautonomous problems

In this paper we consider the nonlocal nonautonomous evolution problem ∂tu=−u+g(Ku,t)inΩwithu=0inRN∖Ω,where Ω is a smooth bounded domain in RN, g:R2→R and K is an integral operator with a symmetric kernel. We prove existence and some regularity properties of the pullback attractor. We also show addi...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten Vol. 294; no. 11; pp. 2063 - 2079
Main Authors: Bezerra, Flank D. M., da Silva, Severino H., Pereira, Antônio L.
Format: Journal Article
Language:English
Published: Weinheim Wiley Subscription Services, Inc 01-11-2021
Subjects:
Asymptotic properties
evolution process
nonautonomous equations
nonlocal diffusion equations
pullback attractors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider the nonlocal nonautonomous evolution problem ∂tu=−u+g(Ku,t)inΩwithu=0inRN∖Ω,where Ω is a smooth bounded domain in RN, g:R2→R and K is an integral operator with a symmetric kernel. We prove existence and some regularity properties of the pullback attractor. We also show additional forward asymptotic results in the asymptotically autonomous case, using the properties of the Lyapunov functional for the limiting problem.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201900296