Existence and continuity of global attractors and nonhomogeneous equilibria for a class of evolution equations with non local terms

In this paper, we are concerned with some aspects of the asymptotic behavior of the dynamical system generated by evolution equations with nonlocal terms of the type ∂ u ( x , t ) ∂ t = − u ( x , t ) + g ( β ( K u ) ( x , t ) ) , x ∈ Ω , t > 0 where Ω ⊂ R N , β > 0 , N ≥ 1 is a bounded smooth domain and K is an integral operator with symmetric kernel ( K u ) ( x ) ≔ ∫ R N J ( x , y ) u ( y ) d y .