Nonclassical diffusion equations on with singularly oscillating external forces

We consider for ρ ∈ [ 0 , 1 ) and ε > 0 , the nonclassical diffusion equation on R N ( N ≥ 3 ) with a singularly oscillating external force, u t − Δ u t − Δ u + f ( x , u ) + λ u = g 0 ( x , t ) + ε − ρ g 1 ( t / ε ) , together with equation u t − Δ u t − Δ u + λ u + f ( x , u ) = g 0 ( x , t ) formally corresponding to the limiting case ε = 0 . Under suitable assumptions on the external force, the uniform (w.r.t. ε ) boundedness of the related uniform attractors A ε is established as well as the convergence of the attractor A ε of the first equation to the attractor A 0 of the second one as ε → 0 + .