Asymptotic behavior for a class of nonlocal nonautonomous problems

Flank D. M. Bezerra, Severino H. da Silva and Antônio L. Pereira

Mathematische Nachrichten, 2021, vol. 294, issue 11, 2063-2079

Abstract: 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.

Date: 2021
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https://doi.org/10.1002/mana.201900296

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:294:y:2021:i:11:p:2063-2079

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