Oscillatory traveling waves in a quasi-linear hyperbolic system in traffic flow
Abstract
We prove the existence of oscillatory traveling wave solutions in a quasi-linear hyperbolic system with relaxation and diffusion in traffic flow when the diffusion is dominant. The innovation of the paper is to construct invariant regions to contain the oscillatory trajectories connecting the saddle and the stable spiral. We also prove that the oscillatory traveling wave solutions are linearly unstable against perturbations.
Fields of Study & Subjects
Traffic control and management
Advanced Differential Equations and Dynamical Systems
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 31
- Issue
- 0
- Pages
- 252–263
- Publication date
- 5 March 2026
- Language
- EN