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 | |
| Source Publication | ADVANCED NONLINEAR STUDIES
 |
| ISSN | 1536-1365 |
| Volume | 21Issue:3Pages:633-660 |
| Abstract | 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. |
| Keyword | Wave Equation Variational Method Klein-Gordon System Periodic Solutions |
| DOI | 10.1515/ans-2021-2138 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000682145500007 |
| Publisher | WALTER DE GRUYTER GMBH |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59021 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Chen, Jianyi |
| Affiliation | 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 |
| Recommended Citation 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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