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Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

Published online by Cambridge University Press:  20 November 2018

Liangliang Li ,
Jing Tian  and
Goong Chen
Liangliang Li
Affiliation:
IFCEN, Sun Yat-sen University, Zhuhai, 519082, China, e-mail : liliangliang@mail.sysu.edu.cn
Jing Tian
Affiliation:
Department of Mathematics, Towson University, Towson, MD 21252, United States, e-mail : jtian@towson.edu
Goong Chen
Affiliation:
Department of Mathematics and Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843-4242, United States, e-mail : gchen@math.tamu.edu
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Abstract

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The study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

Keywords

32H5034C2837K5054H2058J45chaotic vibrationreflection boundary conditionperiod-doubling bifurcationmethod of characteristics
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 768 - 786
Copyright
Copyright © Canadian Mathematical Society 2018

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