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DYNAMICS OF NONLOCAL KURAMOTO–SIVASHINSHY EQUATIONS WITH MULTIPLICATIVE WHITE NOISE

Part of: Partial differential equations Infinite-dimensional dissipative dynamical systems Stochastic analysis

Published online by Cambridge University Press:  23 October 2025

XIAOPENG CHEN Open the ORCID record for XIAOPENG CHEN [Opens in a new window]  and
HAN GAO
XIAOPENG CHEN*
Affiliation:
Department of Mathematics, Shantou University , Guangdong, Shantou 515063, China; e-mail: 21hgao@stu.edu.cn
HAN GAO
Affiliation:
Department of Mathematics, Shantou University , Guangdong, Shantou 515063, China; e-mail: 21hgao@stu.edu.cn
*
e-mail: xpchen@stu.edu.cn
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Abstract

We study the long time dynamic properties of the nonlocal Kuramoto–Sivashinsky (KS) equation with multiplicative white noise. First, we consider the dynamic properties of the stochastic nonlocal KS equation via a transformation into the associated conjugated random differential equation. Next, we prove the existence and uniqueness of solution for the conjugated random differential equation in the theory of random dynamical systems. We also establish the existence and uniqueness of a random attractor for the stochastic nonlocal equation.

Keywords

random attractornonlocal Kuramoto–Shivashinsky equationwhite noiserandom dynamical systems

MSC classification

Primary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations
Secondary: 35B40: Asymptotic behavior of solutions 60H15: Stochastic partial differential equations

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 67 , 2025 , e34
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of the Australian Mathematical Publishing Association Inc.

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Footnotes

This paper is dedicated to Professor Tony Roberts

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