Statistical solutions and piecewise Liouville theorem four impulsive discrete nonlinear Schrödinger-Boussinesq equations. (Chinese. English summary) Zbl 07801753

Zhang, Yongkang; Huang, Zhongyu; Zhao, Caidi

Acta Math. Appl. Sin. 46, No. 4, 565-589 (2023).

Summary: In this paper, we study the initial value problem and the existence of statistical solutions for impulsive discrete nonlinear Schrödinger-Boussinesq equations. The authors first prove the global well-posedness of the impulsive problem, then prove that the process generated by the solutions operator possesses pullback attractors and a family of invariant Borel probability measures. Then we give the definition of statistical solutions for the impulsive problem and prove its existence. The results show that the statistical solution of the impulsive problem satisfies satisfies merely the Liouville type theorem piecewise.

MSC:

35B41	Attractors
34D35	Stability of manifolds of solutions to ordinary differential equations
76F20	Dynamical systems approach to turbulence
39A12	Discrete version of topics in analysis

Keywords:

discrete nonlinear Schrödinger-Boussinesq equations; statistical solution; piecewise Liouville theorem; impulsive differential equation; pullback attractor

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