Xiang Qiaomin, Yang Qigui
School of Mathematics and Big Data, Foshan University, Foshan 528000, People's Republic of China.
School of Mathematics, South China University of Technology, Guangzhou 510000, People's Republic of China.
Chaos. 2020 Feb;30(2):023127. doi: 10.1063/1.5139910.
Little seems to be known about the chaos of the two-dimensional (2D) hyperbolic partial differential equations (PDEs). The objective of this paper is to study the nonisotropic chaotic vibrations of a system governed by a 2D linear hyperbolic PDE with mixed derivative terms (MDTs) and a nonlinear boundary condition (NBC), where the interaction between MDTs and NBC causes the energy of such a system to rise and fall. The 2D hyperbolic system is proved to be topologically conjugate with the corresponding Riemann invariants, which are rigorously proved to be chaotic. Two numerical examples are carried out to demonstrate the theoretical results.
关于二维（2D）双曲型偏微分方程（PDEs）的混沌现象，人们所知甚少。本文的目的是研究一个由带有混合导数项（MDTs）的二维线性双曲型PDE和一个非线性边界条件（NBC）所支配的系统的非各向同性混沌振动，其中MDTs和NBC之间的相互作用导致该系统的能量起伏。二维双曲型系统被证明与相应的黎曼不变量在拓扑上共轭，而黎曼不变量被严格证明是混沌的。给出了两个数值例子来验证理论结果。
