Random attractors and their stability for nonclassical diffusion equations driven by additive white noise with delay and intensity

In this article, we study the asymptotic behavior of solutions of nonclassical diffusion equation driven by an additive noise with delay and intensity \(\epsilon\in(0,1]\) on \(\mathbb{R}^n\). We first establish the existence and uniqueness of tempered pullback random attractors for the equations in \(C([-\rho,0],H^{1}(\mathbb{R}^n))\), and then the upper semicontinuity of random attractors is also obtained when the intensity of noise approaches zero. It's worth mentioning that the Arzela-Ascoli theorem, spectral decomposition, and uniform tail-estimates have been utilized to demonstrate the asymptotic compactness of the solutions. For more information see https://ejde.math.txstate.edu/Volumes/2025/40/abstr.html