Random attractors and their stability for nonclassical diffusion equations driven by additive white noise with delay and intensity
Year: 2025
Type: article
Abstract: 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
Authors: Wenhui Ma, Qiaozhen Ma
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409377752