Statistical solution and Liouville type theorem for the Klein-Gordon-Schrodinger equations

被引：47
|
作者：
Zhao, Caidi [1 ]
Caraballo, Tomas [2 ]
Lukaszewicz, Grzegorz [3 ]
机构：
[1] Wenzhou Univ, Dept Math, Wenzhou 325035, Zhejiang, Peoples R China
[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Fac Matemat, C Tarfia S-N, Seville 41012, Spain
[3] Univ Warsaw, Inst Appl Math & Mech, Banacha 2, PL-02097 Warsaw, Poland
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 281卷
关键词：
Klein-Gordon-Schodinger equations; Statistical solution; Pullback attractor; Invariant measure; Liouville type theorem;
D O I：
10.1016/j.jde.2021.01.039
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, the authors investigate the system of Schrodinger and Klein-Gordon equations with Yukawa coupling. They first prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satisfies a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem. (C) 2021 Elsevier Inc. All rights reserved.
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页码：1 / 32
页数：32
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