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 ${A_{ε} (t)}_{t \in R}$ to equation (1.1) with $ε \in [0, 1]$ .

Keywords

Nonclassical diffusion equations upper semicontinuity pullback attractors delay

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