KMS Of Academy of mathematics and systems sciences, CAS
Periodic Solutions to Klein-Gordon Systems with Linear Couplings | |
Chen, Jianyi1; Zhang, Zhitao2,3,4; Chang, Guijuan1; Zhao, Jing1 | |
2021-08-01 | |
发表期刊 | ADVANCED NONLINEAR STUDIES |
ISSN | 1536-1365 |
卷号 | 21期号:3页码:633-660 |
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. |
关键词 | Wave Equation Variational Method Klein-Gordon System Periodic Solutions |
DOI | 10.1515/ans-2021-2138 |
收录类别 | SCI |
语种 | 英语 |
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 |
WOS类目 | Mathematics, Applied ; Mathematics |
WOS记录号 | WOS:000682145500007 |
出版者 | WALTER DE GRUYTER GMBH |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/59021 |
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.Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China 2.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100049, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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. |
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