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

被引：51

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.

引用

页码：1 / 32

页数：32

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