In this paper, we consider a class of nonclassical diffusion equations on R N with hereditary memory, in presence of singularly oscillating external forces depending on a positive parameter and a new class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. Under a general assumption on the memory kernel and for a very large class of nonlinearities, we prove the existence of uniform attractors in H 1 (R N) × L 2 (R + , H 1 (R N)). The uniform boundedness (w.r.t.) and the convergence of uniform attractors  as tends to 0 are also studied. Our results extend and improve some results in Anh and Toan.

Abstract. We prove the existence of uniform attractors Aε in the space H 1 (R N )∩L p (R N ) for the following non-autonomous nonclassical diffusion equations on R N ,The upper semicontinuity of the uniform attractors {Aε} ε∈ [0,1] at ε = 0 is also studied.