Existence of chaotic oscillations in second-order linear hyperbolic PDEs with implicit boundary conditions

被引：12
作者：
Yang, Qigui [1 ]
Xiang, Qiaomin [1 ]
机构：
[1] South China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 457卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Chaotic oscillation; Hyperbolic PDE; Implicit boundary condition; Perturbation; DIMENSIONAL WAVE-EQUATION; SCRAMBLED SET; VIBRATIONS; VAN; HYSTERESIS; OPERATORS;
D O I：
10.1016/j.jmaa.2017.08.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper establishes rigorously mathematical theorems that guarantee the existence of chaotic oscillations in the systems of second-order linear hyperbolic PDEs. It separately considers the systems with nonlinear explicit boundary conditions (EBCs) and nonlinear implicit boundary conditions (IBCs) as well as those with such IBCs subjected to small perturbations, where IBCs include EBCs as special cases but the latter cannot in general be expressed by the former. Numerical examples are demonstrated to illustrate the effectiveness of theoretical results. (c) 2017 Elsevier Inc. All rights reserved.
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页码：751 / 775
页数：25
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