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

Caidi Zhao, Huite Jiang and Tomás Caraballo

Applied Mathematics and Computation, 2021, vol. 404, issue C

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.

Keywords: Statistical solution; Impulsive lattice system; Reaction-diffusion equation; Piecewise Liouville theorem; Pullback attractor (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:404:y:2021:i:c:s009630032100151x

DOI: 10.1016/j.amc.2021.126103

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