Nonclassical diffusion equations on RNRN with singularly oscillating external forces

We consider for ρ∈[0,1)ρ∈[0,1) and ε>0ε>0, the nonclassical diffusion equation on RN(N≥3)RN(N≥3) with a singularly oscillating external force, ut−Δut−Δu+f(x,u)+λu=g0(x,t)+ε−ρg1(t/ε),ut−Δut−Δu+f(x,u)+λu=g0(x,t)+ε−ρg1(t/ε), together with equation ut−Δut−Δu+λu+f(x,u)=g0(x,t)ut−Δut−Δu+λu+f(x,u)=g0(x,t) formally corresponding to the limiting case ε=0ε=0. Under suitable assumptions on the external force, the uniform (w.r.t. εε) boundedness of the related uniform attractors AεAε is established as well as the convergence of the attractor AεAε of the first equation to the attractor A0A0 of the second one as ε→0+ε→0+.