Pullback attractors for a class of non-autonomous nonclassical diffusion equations Original Research Article

We consider the first initial boundary value problem for the non-autonomous nonclassical diffusion equation ut−εΔut−Δu+f(u)=g(t)ut−εΔut−Δu+f(u)=g(t), ε∈[0,1]ε∈[0,1], in a bounded domain in RNRN. Under a Sobolev growth rate of the nonlinearity ff and a suitable exponential growth of the external force gg, using the asymptotic a priori estimate method, we prove the existence of pullback DD-attractors View the MathML sourceAεˆ in the space View the MathML sourceH01(Ω) and the upper semicontinuity of View the MathML sourceAεˆ at ε=0ε=0.