Upper semicontinuity of pullback attractors for nonclassical diffusion equations with delay

Abstract

In this paper, we mainly study the upper semicontinuity of pullback D-attractors for a nonclassical diffusion equation with delay term b ( t , u t ) which contains some hereditary characteristics. Under a critical nonlinearity f, a time-dependent force g ( t , x ) with exponential growth and a delayed force term b ( t , u t ), using the asymptotic a priori estimate method, we prove the upper semicontinuity of pullback D-attractor { A ε ( t ) } t ∈ R to equation (1.1) with ε ∈ [ 0 , 1 ].