LAUSR

In this work we study the pullback dynamics of a class of nonlocal nonautonomous evolution equations for neural fields in a bounded smooth domain Ω in RN ∂tu(t, x) = −u(t, x) + ∫ RN J(x, y) f (t, u(t, y))dy, t ≥ τ, x ∈ Ω, u(τ, x) = uτ(x), x ∈ Ω, with u(t, x) = 0, t ≥ τ, x ∈ RN\Ω, where the integrable function J : RN ×RN → R is continuously differentiable, ∫ RN J(x, y)dy = ∫ RN J(x, y)dx = 1 and symmetric i.e., J(x, y) = J(y, x) for any x, y ∈ RN . Under suitable assumptions on the nonlinearity f : R2 → R, we prove existence, regularity and upper semicontinuity of pullback attractors for the evolution process associated to this problem.