论文信息 - Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

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

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.

Liangliang Li | Goong Chen | Jing Tian

[1] M. Xiao,et al. Numerical methods for weak solution of wave equation with van der Pol type nonlinear boundary conditions , 2016 .

[2] F. Colombini,et al. Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time , 1983 .

[3] Ferruccio Colombini,et al. An example of a weakly hyperbolic Cauchy problem not well posed inC∞ , 1982 .

[4] S. Spagnolo,et al. Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps , 1979 .

[5] Yu Huang,et al. Nonisotropic spatiotemporal chaotic vibrations of the one- dimensional wave equation with a mixing transport term and general nonlinear boundary condition , 2010 .

[6] W. A. Coppel,et al. Dynamics in One Dimension , 1992 .

[7] Tingwen Huang,et al. Chaotic Behavior of Interval Maps and Total Variations of iterates , 2004, Int. J. Bifurc. Chaos.

[8] Guanrong Chen,et al. Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. Part I: Controlled hysteresis , 1998 .