College of Mathematics and Statistics
Northwest Normal University
Lanzhou, China
email: ma15193089786@163.com
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, China
email: maqzh@nwnu.edu.cn
Wenhui Ma, Qiaozhen Ma
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.
Submitted October 2, 2024. Published April 11, 2025.
Math Subject Classifications: 35B40, 35B41, 35R60, 37L55.
Key Words: Pullback random attractors; nonclassical diffusion equation; nonlinear delay; additive white noise
DOI: 10.58997/ejde.2025.40
Show me the PDF file (408 KB), TEX file for this article.
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Wenhui Ma College of Mathematics and Statistics Northwest Normal University Lanzhou, China email: ma15193089786@163.com |
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Qiaozhen Ma College of Mathematics and Statistics Northwest Normal University Lanzhou, China email: maqzh@nwnu.edu.cn |
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