脉冲离散Ginzburg-Landau方程组的统计解及其极限行为

摘要/Abstract

摘要：

该文研究脉冲离散Ginzburg-Landau方程组的统计解及其极限行为.文章首先证明该脉冲离散方程组的全局适定性，接着证明由解算子生成的过程存在拉回吸引子和一族Borel不变概率测度，然后给出该脉冲离散方程组统计解的定义并证明其存在性.该文的结果揭示了脉冲系统的统计解只分段地满足Liouville型定理.最后，文章证明了脉冲离散Ginzburg-Landau方程组的统计解收敛于脉冲离散Schrödinger方程组的统计解.

关键词: 统计解, 脉冲微分方程, Liouville型定理, 离散耦合Ginzburg-Landau方程, 离散Schrödinger方程

Abstract:

In this article we first prove the global well-posedness of the impulsive discrete Ginzburg-Landau equations. Then we establish that the generated process by the solution operators possesses a pullback attractor and a family of invariant Borel probability measures. Further, we formulate the definition of statistical solution for the addressed impulsive system and prove the existence. Our results reveal that the statistical solution of the impulsive system satisfies merely the Liouville type theorem piecewise, which implies that the Liouville type equation for impulsive system will not always hold true on the interval containing any impulsive point. Finally, we prove that the statistical solution of the impulsive discrete Ginzburg-Landau equations converges to that of the impulsive discrete Schrödinger equations.

Key words: Statistical solution, Impulsive differential equation, Liouville type theorem, Discrete complex Ginzburg-Landau equation, Discrete Schrödinger equation

中图分类号:

O175.8

赵才地,姜慧特,李春秋,TomásCaraballo. 脉冲离散Ginzburg-Landau方程组的统计解及其极限行为[J]. 数学物理学报, 2022, 42(3): 784-806.

Caidi Zhao,Huite Jiang,Chunqiu Li,Caraballo Tomás. Statistical Solutions and Its Limiting Behavior for the Impulsive Discrete Ginzburg-Landau Equations[J]. Acta mathematica scientia,Series A, 2022, 42(3): 784-806.

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