Statistical solution and piecewise Liouville theorem for the impulsive discrete Zakharov equations

Abstract

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.

Keywords

• statistical solution
• impulsive discrete zakharov equation
• liouville type theorem
• pullback attractor