In this talk, I will mainly discuss the chaotic vibration phenomenon of the 2D non-strictly hyperbolic equation due to an energy-injection boundary condition and a distributed self-regulation boundary condition. By using the method of characteristics, we give a rigorous proof of the chaotic vibration phenomenon of the 2D non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs by applying the period-doubling bifurcation theorem. Numerical simulations will be provided.

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