Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation. Issue 4 (1st December 2018)

• Record Type: Journal Article
• Authors: Li, Liangliang; Tian, Jing; Chen, Goong
• Is Part Of: Canadian mathematical bulletin =. Volume 61:Issue 4(2018)
• Page Start: 768
• Page End: 786
• Publication Date: 2018-12-01
• Subjects: 32H50 -- 34C28 -- 37K50 -- 54H20 -- 58J45; chaotic vibration -- reflection boundary condition -- period-doubling bifurcation -- method of characteristics; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2018-012-1
• Languages: English
• ISSNs: 0008-4395

Abstract

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.