Statistical solution and Kolmogorov entropy for the impulsive discrete Klein-Gordon-Schrödinger-type equations

Zehan Lin; Chongbin Xu; Caidi Zhao; Chujin Li

doi:10.3934/dcdsb.2022065

Article Contents

2023, Volume 28, Issue 1: 20-49. Doi: 10.3934/dcdsb.2022065

This issue Previous Article Semigroup property of fractional differential operators and its applications Next Article A novel numerical method based on a high order polynomial approximation of the fourth order Steklov equation and its eigenvalue problems

Statistical solution and Kolmogorov entropy for the impulsive discrete Klein-Gordon-Schrödinger-type equations

1.
Department of Mathematics, Wenzhou University, Wenzhou, 325035, China
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei Province, 430071, China

^* Corresponding author: Caidi Zhao
^* Corresponding author: Caidi Zhao

Received: November 30, 2021

Early access: March 2022

Published: January 2023

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Abstract

This paper studies the impulsive discrete Klein-Gordon-Schrödinger-type equations. We first prove that the problem of the discrete Klein-Gordon-Schrödinger-type equations with initial and impulsive conditions is global well-posedness. Then we establish that the solution operators form a continuous process and that this process possesses a pullback attractor and a family of invariant Borel probability measures. Further, we prove that this family of Borel probability measures satisfies the Liouville type theorem piecewise and is a statistical solution of the impulsive discrete Klein-Gordon-Schrödinger-type equations. Finally, we formulate the concept of Kolmogorov entropy for the statistical solution and estimate its upper bound.

Keywords:

Statistical solution,
Impulsive differential equation,
Liouville type theorem,
Discrete Klein-Gordon-Schrödinger-type equation,
Kolmogorov entropy.

Mathematics Subject Classification: 35B41, 35D99, 76F20.

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References

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