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

  • Liangliang Li (a1), Jing Tian (a2) and Goong Chen (a3)

Abstract

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.

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

  • Liangliang Li (a1), Jing Tian (a2) and Goong Chen (a3)

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