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Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices

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  • Zhao, Caidi
  • Jiang, Huite
  • Caraballo, Tomás

Abstract

We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of Borel invariant probability measures. Furthermore, we formulate the definition of statistical solution for the addressed impulsive system and prove the existence. Our results show that the statistical solution of the impulsive system satisfies merely the Liouville type theorem piecewise, and the Liouville type equation for impulsive system will not always hold true on the interval containing any impulsive point.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s009630032100151x
    DOI: 10.1016/j.amc.2021.126103
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hujun Yang & Xiaoling Han & Caidi Zhao, 2022. "Homogenization of Trajectory Statistical Solutions for the 3D Incompressible Micropolar Fluids with Rapidly Oscillating Terms," Mathematics, MDPI, vol. 10(14), pages 1-15, July.

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