PULLBACK ATTRACTORS AND INVARIANT MEASURES FOR THE DISCRETE ZAKHAROV EQUATIONS

Zeqi Zhu; Yanmiao Sang; Caidi Zhao

doi:10.11948/20190091

2019 Volume 9 Issue 6

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Zeqi Zhu, Yanmiao Sang, Caidi Zhao. PULLBACK ATTRACTORS AND INVARIANT MEASURES FOR THE DISCRETE ZAKHAROV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2333-2357. doi: 10.11948/20190091

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Zeqi Zhu, Yanmiao Sang, Caidi Zhao. PULLBACK ATTRACTORS AND INVARIANT MEASURES FOR THE DISCRETE ZAKHAROV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2333-2357. doi: 10.11948/20190091

PULLBACK ATTRACTORS AND INVARIANT MEASURES FOR THE DISCRETE ZAKHAROV EQUATIONS

1.
State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, 430071, Wuhan, China
2.
Department of Mathematics, Wenzhou University, Wenzhou, 325035, Zhejiang, China

Corresponding author: Email address: zhaocaidi2013@163.com(C. Zhao)
Fund Project: The authors are supported by NSF of China(Nos. 51279202, 11271290) and by NSF of Zhejiang Province(No. LY17A010011)

Abstract

Abstract

This article studies the probability distributions of solutions in the phase space for the discrete Zakharov equations. The authors first prove that the generated process of the solutions operators possesses a pullback-${\mathcal D}$ attractor, and then they establish that there exists a unique family of invariant Borel probability measures supported by the pullback attractor.
- Invariant measure /
- pullback attractor /
- discrete Zakharov equations
MSC: 35B41, 37Lxx, 35Qxx

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References

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