Open Access
August, 2023 Asymptotic Behavior of Random Reaction-diffusion Delay Equations Driven by Colored Noise
Wenjun Ma, Qiaozhen Ma
Author Affiliations +
Taiwanese J. Math. 27(4): 759-798 (August, 2023). DOI: 10.11650/tjm/230301

Abstract

In this paper, we consider the asymptotic behavior of random reaction-diffusion delay equations driven by colored noise defined on unbounded domains. We firstly establish the existence and uniqueness of pullback random attractors for the continuous cocycle associated with the equation, and then consider the convergence of random attractors when colored noise approximates white noise. The methods of uniform tail-estimate and operator decomposition are employed to obtain the pullback asymptotic compactness of the solutions in order to overcome the non-compactness of the Sobolev embeddings on unbounded domains.

Funding Statement

This work is supported by NSFC (11961059).

Citation

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Wenjun Ma. Qiaozhen Ma. "Asymptotic Behavior of Random Reaction-diffusion Delay Equations Driven by Colored Noise." Taiwanese J. Math. 27 (4) 759 - 798, August, 2023. https://doi.org/10.11650/tjm/230301

Information

Received: 17 October 2022; Revised: 25 February 2023; Accepted: 5 March 2023; Published: August, 2023
First available in Project Euclid: 20 March 2023

MathSciNet: MR4617932
zbMATH: 07734111
Digital Object Identifier: 10.11650/tjm/230301

Subjects:
Primary: 35B40 , 60H15

Keywords: colored noise , random attractor , reaction-diffusion equation , White noise

Rights: Copyright © 2023 The Mathematical Society of the Republic of China

Vol.27 • No. 4 • August, 2023
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