Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven By Locally Lipschitz Lévy Noises

Authors

https://doi.org/10.61383/ejam.20242165

Keywords:

Selkov systems, Weak pullback mean random attractor, Lévy noises

Abstract

This paper is concerned with weak pullback mean random attractor of reversible Selkov lattice systems defined on the entire integer set \(\mathbb{Z}\) driven by locally Lipschitz Lévy noises. Firstly, we formulate the stochastic lattice equations to an abstract system defined in the non-concrete space \(\ell^2\times\ell^2\) of square-summable sequences. Secondly, we establish the global well-posedness of the systems with locally Lipschitz diffusion terms. Under certain conditions, we show that the long-time dynamics can be captured by a weakly compact and weakly attracting mean random attractor in the Bochner space \(L^2(\Omega,\ell^2\times\ell^2)\). To overcome the difficulty caused by the drift and diffusion terms, we adopt a stopping time technique to prove the convergence of solutions in probability. The mean random dynamical systems theory proposed by Wang (J. Differ. Equ., 31:2177-2204, 2019) is used to deal with the difficulty caused by the nonlinear noise.

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Published

2024 Mar 25

How to Cite

[1]
G. Li, X. Yang, L. Zhou, and Y. Wang, “Weak Mean Random Attractor of Reversible Selkov Lattice Systems Driven By Locally Lipschitz Lévy Noises”, Electron. J. Appl. Math., vol. 2, no. 1, pp. 40–63, Mar. 2024.

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Vol. 2 No. 1 (2024)

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Research Article

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Copyright (c) 2024 Guofu Li, Xiulan Yang, Liguang Zhou; Yan Wang (Corresponding Author)

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This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
 
 
Received 2023 Sep 09
Accepted 2024 Mar 10
Published 2024 Mar 25