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

Binbin Miao; Chongbin Xu; Caidi Zhao; Binbin Miao; Chongbin Xu; Caidi Zhao

doi:10.3934/math.2022505

AIMS Mathematics

2022, Volume 7, Issue 5: 9089-9116. doi: 10.3934/math.2022505

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Research article

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

Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang Province, 325035, China

Received: 13 October 2021 Revised: 27 February 2022 Accepted: 28 February 2022 Published: 08 March 2022
MSC : 35B41, 34D35, 76F20

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.
- statistical solution,
- impulsive discrete Zakharov equation,
- Liouville type theorem,
- pullback attractor
Citation: Binbin Miao, Chongbin Xu, Caidi Zhao. Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations[J]. AIMS Mathematics, 2022, 7(5): 9089-9116. doi: 10.3934/math.2022505

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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.

References

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