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Invariant Borel probability measures for discrete long-wave-short-wave resonance equations

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  • Wang, Chengzhi
  • Xue, Gang
  • Zhao, Caidi

Abstract

In this article we study the Borel probability measures that can be associated to the time averaged observation of the process generated by the non-autonomous long-wave-short-wave resonance equations on infinite lattices, via the notion of generalized Banach limit. We establish that the generated process possesses a pullback-D attractor, and further prove that there exists a unique family of invariant Borel probability measures carried by the pullback attractor.

Suggested Citation

  • Wang, Chengzhi & Xue, Gang & Zhao, Caidi, 2018. "Invariant Borel probability measures for discrete long-wave-short-wave resonance equations," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 853-865.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:853-865
    DOI: 10.1016/j.amc.2018.06.059
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    Cited by:

    1. Zhao, Caidi & Jiang, Huite & Caraballo, Tomás, 2021. "Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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