Open AccessStatistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations
Author(s) -
Binbin Miao,
Che Xu,
Caidi Zhao
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022505
Subject(s) - pullback attractor , mathematics , piecewise , invariant (physics) , pullback , attractor , pure mathematics , mathematical analysis , mathematical physics
This article studies the discrete Zakharov equations with impulsive effect. The authors first prove that the problem is global well-posed and that the process formed by the solution operators possesses a pullback attractor. Then they establish that there is a family of invariant Borel probability measures contained in the pullback attractor, and that this family of measures satisfies the Liouville type theorem piecewise and is a statistical solution of the impulsive discrete Zakharov equations.