脉冲离散Ginzburg-Landau方程组的统计解及其极限行为

Abstract

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

CLC Number:

O175.8

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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Statistical Solutions and Its Limiting Behavior for the Impulsive Discrete Ginzburg-Landau Equations

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