In this paper, we consider a non-autonomous nonlocal reactiondiffusionequation with a small perturbation in the nonlocal diffusion termand the non-autonomous force. Under the assumptions imposed on the viscosity function, the uniqueness of weak solutions cannot be guaranteed. In this multi-valued framework, the existence of weak solutions and minimal pullback attractors in the L2-norm are analysed. In addition, some relationships between the attractors of the universe of fixed bounded sets and those associated to a universe given by a tempered condition are established. Finally, the upper semicontinuity property of pullback attractors w.r.t. the parameter is proved. Indeed, under suitable assumptions, we prove that the family of pullback attractors converges to the corresponding global compact attractor associated to the autonomous nonlocal limit problem when the parameter goes to zero.
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