Existence, regularity and upper semicontinuity of pullback attractors for the evolution process associated to a neural field model

摘要

In this work we study the pullback dynamics of a class of nonlocal nonautonomous evolution equations for neural fields in a bounded smooth domain W in RN with u(t, x) = 0, t ≥ t, x 2 RNnW, where the integrable function J : RN × RN ! R is continuously differentiable, RRN J(x, y)dy = RRN J(x, y)dx = 1 and symmetric i.e.,J(x, y) = J(y, x) for any x, y 2 RN. Under suitable assumptions on the nonlinearityf : R2 ! R, we prove existence, regularity and upper semicontinuity of pullbackattractors for the evolution process associated to this problem.