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1 results

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

  • Liangliang Li, Jing Tian, Goong Chen
  • Journal:
    Canadian Mathematical Bulletin / Volume 61 / Issue 4 / 01 December 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 768-786
    Print publication:
    01 December 2018
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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.