Book chapter
Zero Relaxation Limit for a Non-Strictly Hyperbolic System Arising in Traffic Flow with Dominant Diffusion
Analysis and PDE in Latin America, pp.101-109
Trends in Mathematics, 15, Springer Nature Switzerland
2026
DOI: 10.1007/978-3-031-99557-6_13
Abstract
In this paper, we prove the existence of the zero relaxation limit solution for a non-strictly hyperbolic system of conservation laws with relaxation arising in traffic flow that exhibits dominant diffusion. Our approach is based on the vanishing viscosity method. We construct an invariant region that provides L∞ $$L^{\infty }$$ a priori estimates on the sequence of viscous solutions, and we use the theory of compensated compactness to study the limit as the diffusion parameter tends to zero. Our analysis includes the vacuum state.
Details
- Title: Subtitle
- Zero Relaxation Limit for a Non-Strictly Hyperbolic System Arising in Traffic Flow with Dominant Diffusion
- Creators
- José David Beltrán - University of IowaTong Li - University of Iowa
- Contributors
- Duván Cardona Sanchez (Editor)Brian Grajales (Editor)
- Resource Type
- Book chapter
- Publication Details
- Analysis and PDE in Latin America, pp.101-109
- Series
- Trends in Mathematics; 15
- DOI
- 10.1007/978-3-031-99557-6_13
- eISSN
- 2297-024X
- ISSN
- 2297-0215
- Publisher
- Springer Nature Switzerland; Cham
- Language
- English
- Date published
- 2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985112977702771
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