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

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

作　　者：张天伟 李永昆[1] Zhang Tianwei;Li Yongkun(School of Mathematics and Statistics,Yunnan University,Kunming 650500)

机构地区：[1]云南大学数学与统计学院,昆明650500

出　　处：《数学物理学报（A辑）》2024年第2期326-353,共28页Acta Mathematica Scientia

基　　金：国家自然科学基金(12261098,11861072)。

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.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.

关 键 词：Schrödinger KLEIN-GORDON GALERKIN方法 FOURIER级数 Picard迭代 

分 类 号：O175.26[理学—数学]