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Research Article | Open Access

Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations

Binbin Miao, Chongbin Xu, Caidi Zhao( )
Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang Province, 325035, China
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Abstract

This article studies the discrete Zakharov equations with impulsive effect. The authors first prove that the problem is global well-posed and that the process formed by the solution operators possesses a pullback attractor. Then they establish that there is a family of invariant Borel probability measures contained in the pullback attractor, and that this family of measures satisfies the Liouville type theorem piecewise and is a statistical solution of the impulsive discrete Zakharov equations.

Keywords

statistical solutionimpulsive discrete Zakharov equationLiouville type theorempullback attractor
CLC number: 35B41, 34D35, 76F20

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9089-9116
DOI: 10.3934/math.2022505

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Cite this article:
Miao B, Xu C, Zhao C. Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations. AIMS Mathematics, 2022, 7(5): 9089-9116. https://doi.org/10.3934/math.2022505

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Received: 13 October 2021
Revised: 27 February 2022
Accepted: 28 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

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