带有非局部 Laplace 算子的饱和 Schrödinger-Klein-Gordon 方程的概自守动力学

数学物理学报 ›› 2024, Vol. 44 ›› Issue (2): 326-353.

带有非局部 Laplace 算子的饱和 Schrödinger-Klein-Gordon 方程的概自守动力学

张天伟(),李永昆^*()

云南大学数学与统计学院昆明 650500

收稿日期:2022-06-08 修回日期:2023-10-07 出版日期:2024-04-26 发布日期:2024-04-07
通讯作者: * 李永昆,Email: yklie@ynu.edu.cn
作者简介:张天伟,Email:yntwzhang@outlook.com
基金资助:
国家自然科学基金(12261098);国家自然科学基金(11861072)

Almost Automorphic Dynamics of Nonlocal Laplacian Saturating Schrödinger-Klein-Gordon Equations

Zhang Tianwei(),Li Yongkun^*()

School of Mathematics and Statistics, Yunnan University, Kunming 650500

Received:2022-06-08 Revised:2023-10-07 Online:2024-04-26 Published:2024-04-07
Supported by:
NSFC(12261098);NSFC(11861072)

摘要/Abstract

摘要：

迄今为止, 几乎没有学者研究 Schrödinger 或 Klein-Gordon 方程的概自守动力学. 该文结合 Galerkin 方法、 Laplace 变换、Fourier 级数和 Picard 迭代研究了带有非局部 Laplace 算子饱和 Schrödinger-Klein-Gordon 方程的概自守弱解的一些结果. 此外, 还考虑了该方程的全局指数收敛性.

关键词: Schr?dinger, Klein-Gordon, Galerkin 方法, Fourier 级数, Picard 迭代

Abstract:

To the best of the authors' knowledge, almost no literature focuses on the almost automorphic dynamics to Schrödinger or Klein-Gordon equations. This paper gives some results on almost automorphic weak solutions to a nonlocal Laplacian saturating Schrödinger-Klein-Gordon equations by employing a mix of Galerkin method, Laplace transform, Fourier series and Picard iteration. Beyond that, global exponential convergence of the equations is investigated.

Key words: Schr?dinger, Klein-Gordon, Galerkin method, Fourier series, Picard iteration

中图分类号:

O175.26

张天伟, 李永昆. 带有非局部 Laplace 算子的饱和 Schrödinger-Klein-Gordon 方程的概自守动力学[J]. 数学物理学报, 2024, 44(2): 326-353.

Zhang Tianwei, Li Yongkun. Almost Automorphic Dynamics of Nonlocal Laplacian Saturating Schrödinger-Klein-Gordon Equations[J]. Acta mathematica scientia,Series A, 2024, 44(2): 326-353.

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