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Research Article | Open Access

Periodic measures of reaction-diffusion lattice systems driven by superlinear noise

School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China; National Engineering Laboratory of Integrated Transportation Big Data Application Technology, Chengdu, 610031, China
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Abstract

The periodic measures are investigated for a class of reaction-diffusion lattice systems driven by superlinear noise defined on Zk. The existence of periodic measures for the lattice systems is established in l2 by Krylov-Bogolyubov's method. The idea of uniform estimates on the tails of solutions is employed to establish the tightness of a family of distribution laws of the solutions.

Keywords

superlinear noiseperiodic measurereaction-diffusion lattice system

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 35-51
DOI: 10.3934/era.2022002

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Cite this article:
Lin Y. Periodic measures of reaction-diffusion lattice systems driven by superlinear noise. Electronic Research Archive, 2022, 30(1): 35-51. https://doi.org/10.3934/era.2022002

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Received: 18 May 2021
Revised: 09 October 2021
Accepted: 09 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)