脉冲离散非线性Schrodinger-Boussinesq方程组的统计解与分段Liouville型定理  

Statistical Solutions and Piecewise Liouville Theorem four Impulsive Discrete Nonlinear Schrodinger-Boussinesq Equations

作　　者：张永康 黄忠裕[1] 赵才地[1] ZHANG YONGKANG;HUANG ZHONGYU;ZHAO CAIDI(Department of Mathematics,Wenzhou University,Wenzhou 325035,China)

机构地区：[1]温州大学数理学院,温州325035

出　　处：《应用数学学报》2023年第4期565-589,共25页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11971356,11271290);浙江省自然科学基金(LY17A010011)资助项目。

摘　　要：本文研究脉冲离散非线性Schrodinger-Boussinesq方程组的初值问题及其统计解的存在性.作者首先证明该脉冲问题的的整体适定性,然后证明解算子生成的过程存在拉回吸引子和一族不变Borel概率测度,接着给出该脉冲问题统计解的定义并证明其存在性.结果表明,该脉冲问题的统计解只关于时间分段地满足Liouville型定理.In this paper,we study the initial value problem and the existence of statis-tical solutions for impulsive discrete nonlinear Schrodinger-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 fam-ily 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.

关 键 词：离散非线性Schrodinger-Boussinesq方程组 统计解 分段Liouville型定理 脉冲微分方程 拉回吸引子 

分 类 号：O175.8[理学—数学]