ABSTRACT
In this paper, we consider the following nonlocal autonomous evolution equation in a bounded domain Ω in :
where
,
and
are continuously differentiable function, and J is a symmetric kernel; that is,
for any
. 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.
Acknowledgements
The authors are thankful to the anonymous referee for his or her valuable corrections and comments on early version of this work that helped to improve the presentation.
Disclosure statement
No potential conflict of interest was reported by the authors.