Upper semicontinuity for a class of nonlocal evolution equations with Neumann condition. Issue 9 (4th July 2021)

• Record Type: Journal Article
• Authors: Bezerra, Flank D. M.; Sastre-Gomez, Silvia; da Silva, Severino H.
• Is Part Of: Applicable analysis. Volume 100:Issue 9(2021)
• Page Start: 1889
• Page End: 1904
• Publication Date: 2021-07-04
• Subjects: Asymptotic dynamics -- nonlocal equation -- global attractor -- upper semicontinuity; 45J05 -- 45M05 -- 34D45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1671973
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider the following nonlocal autonomous evolution equation in a bounded domain Ω in R N : 1 ∂ t u ( x, t ) = − h ( x ) u ( x, t ) + g ( ∫ Ω J ( x, y ) u ( y, t ) d y ) + f ( x, u ( x, t ) ), where h ∈ W 1, ∞ ( Ω ), g : R → R and f : R N × R → R are continuously differentiable function, and J is a symmetric kernel; that is, J ( x, y ) = J ( y, x ) for any x, y ∈ R N . Under additional suitable assumptions on f and g, we study the asymptotic dynamics of the initial value problem associated to this equation in a suitable phase spaces. More precisely, we prove the existence, and upper semicontinuity of compact global attractors with respect to kernel J .