scientific article; zbMATH DE number 7050465

zbMath1416.35037MaRDI QIDQ4633515

Jing Tian, Liangliang Li, Goong Chen

Publication date: 3 May 2019

Full work available at URL: https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/chaotic-vibration-of-a-twodimensional-nonstrictly-hyperbolic-equation/93957C8C62CCE0019A9F1B1F655B3C92

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

method of characteristicsnonlinear boundary conditionshyperbolicperiod-doubling bifurcationreflection boundary conditiondistributed self-regulating boundary conditionenergy-injecting boundary condition

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Complex behavior and chaotic systems of ordinary differential equations (34C28) Bifurcations in context of PDEs (35B32) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Hyperbolic equations on manifolds (58J45)

Related Items

Chaos of the 2D linear hyperbolic equation with general van der Pol type boundary condition, Chaotic vibration of a two-dimensional wave equation with nonlinear boundary condition, Li-Yorke chaos in weak topology of the \(n\)-dimensional linear systems, Observability and Observers for a Class of Two-Dimensional Hyperbolic PDE Chaotic Systems, Chaotic vibrations of 3D linear hyperbolic PDEs with linear perturbations of superlinear boundary conditions, Observer design and stability analysis for a class of PDE chaotic systems, Chaotic dynamics of a 2D hyperbolic PDE with the boundary conditions of superlinear type, Nonisotropic chaotic vibrations of a 2D hyperbolic PDE

Cites Work

• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• Dynamics in one dimension
• Numerical methods for weak solution of wave equation with van der Pol type nonlinear boundary conditions
• Chaotic vibrations of the one-dimensional wave equation due to a self-excitation boundary condition. Part I: Controlled hysteresis
• CHAOTIC BEHAVIOR OF INTERVAL MAPS AND TOTAL VARIATIONS OF ITERATES
• Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span
• NONISOTROPIC SPATIOTEMPORAL CHAOTIC VIBRATION OF THE WAVE EQUATION DUE TO MIXING ENERGY TRANSPORT AND A VAN DER POL BOUNDARY CONDITION
• Chaotic Vibrations of the One-Dimensional Wave Equation due to a Self-Excitation Boundary Condition.
• Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition.
• Nonisotropic spatiotemporal chaotic vibrations of the one-dimensional wave equation with a mixing transport term and general nonlinear boundary condition
• Unnamed Item
• Unnamed Item
• Unnamed Item