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Periodic Solutions to Klein-Gordon Systems with Linear Couplings

文献类型：期刊论文

作者Chen, Jianyi4; Zhang, Zhitao1,2,3; Chang, Guijuan4; Zhao, Jing4
刊名ADVANCED NONLINEAR STUDIES
出版日期2021-08-01
卷号21期号:3页码:633-660
关键词Wave Equation Variational Method Klein-Gordon System Periodic Solutions
ISSN号1536-1365
DOI10.1515/ans-2021-2138
英文摘要In this paper, we study the nonlinear Klein-Gordon systems arising from relativistic physics and quantum field theories {u(tt) - u(xx) + bu + epsilon v +f(t, x, u) = 0, v(tt) - v(xx) + bv + epsilon u + g(t, x, v) = 0, where u, v satisfy the Dirichlet boundary conditions on spatial interval [0, pi], b > 0 and f, g are 2 pi-periodic in t. We are concerned with the existence, regularity and asymptotic behavior of time-periodic solutions to the linearly coupled problem as e goes to 0. Firstly, under some superlinear growth and monotonicity assumptions on f and g, we obtain the solutions (u(epsilon), v epsilon) with time period 2 pi for the problem as the linear coupling constant e is sufficiently small, by constructing critical points of an indefinite functional via variational methods. Secondly, we give a precise characterization for the asymptotic behavior of these solutions, and show that, as epsilon -> 0, (u(epsilon), v(epsilon)) converge to the solutions of the wave equations without the coupling terms. Finally, by careful analysis which is quite different from the elliptic regularity theory, we obtain some interesting results concerning the higher regularity of the periodic solutions.
资助项目National Natural Science Foundation of China[11701310] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[12026217] ; Natural Science Foundation of Shandong Province[ZR2016AQ04] ; Research Foundation for Advanced Talents of Qingdao Agricultural University[6631114328]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000682145500007
出版者WALTER DE GRUYTER GMBH
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/59020]  
专题中国科学院数学与系统科学研究院
通讯作者Chen, Jianyi
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100049, Peoples R China
3.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China
4.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China
推荐引用方式
GB/T 7714		 Chen, Jianyi,Zhang, Zhitao,Chang, Guijuan,et al. Periodic Solutions to Klein-Gordon Systems with Linear Couplings[J]. ADVANCED NONLINEAR STUDIES,2021,21(3):633-660.
APA Chen, Jianyi,Zhang, Zhitao,Chang, Guijuan,&Zhao, Jing.(2021).Periodic Solutions to Klein-Gordon Systems with Linear Couplings.ADVANCED NONLINEAR STUDIES,21(3),633-660.
MLA Chen, Jianyi,et al."Periodic Solutions to Klein-Gordon Systems with Linear Couplings".ADVANCED NONLINEAR STUDIES 21.3(2021):633-660.

入库方式： OAI收割

来源：数学与系统科学研究院

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