scholarly journals Stability analysis of the numerical Method of characteristics applied to a class of energy-preserving hyperbolic systems. Part II: Nonreflecting boundary conditions

2019 ◽  
Vol 356 ◽  
pp. 267-292
Author(s):  
T.I. Lakoba ◽  
Z. Deng
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Method Of Characteristics ◽  
Hyperbolic Systems ◽  
Nonreflecting Boundary Conditions

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

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe 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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