Nonclassical diffusion equations on RN with singularly oscillating external forces

We consider for rho is an element of [0, 1) and epsilon > 0, the nonclassical diffusion equation on R-N (N >= 3) with a singularly oscillating external force, u(t) - Delta u(t) - Delta u + f (x, u) + lambda u = g(0)(x, t) + epsilon(-rho)g(1)(t/epsilon), together with equation u(t) - Delta u(t) - Delta u + lambda u + f (x, u) = g(0)(x, t) formally corresponding to the limiting case epsilon = 0. Under suitable assumptions on the external force, the uniform (w.r.t. epsilon) boundedness of the related uniform attractors A(epsilon) is established as well as the convergence of the attractor A(epsilon) of the first equation to the attractor A(0) of the second one as epsilon --> 0(+). (C) 2014 Elsevier Ltd. All rights reserved.