Journal article
STABILITY OF TRAVELING WAVES IN QUASI-LINEAR HYPERBOLIC SYSTEMS WITH RELAXATION AND DIFFUSION
SIAM journal on mathematical analysis, Vol.40(3), pp.1058-1075
01/01/2008
DOI: 10.1137/070690638
Abstract
We establish the existence and the stability of traveling wave solutions of a quasi-linear hyperbolic system with both relaxation and diffusion. The traveling wave solutions are shown to be asymptotically stable under small disturbances and under the subcharacteristic condition using a weighted energy method. The delicate balance between the relaxation and the diffusion that leads to the stability of the traveling waves is identified; namely, the diffusion coefficient is bounded by a constant multiple of the relaxation time. Such a result provides an important first step toward the understanding of the transition from stability to instability as parameters vary in physical problems involving both relaxation and diffusion.
Details
- Title: Subtitle
- STABILITY OF TRAVELING WAVES IN QUASI-LINEAR HYPERBOLIC SYSTEMS WITH RELAXATION AND DIFFUSION
- Creators
- Tong Li
- Resource Type
- Journal article
- Publication Details
- SIAM journal on mathematical analysis, Vol.40(3), pp.1058-1075
- Publisher
- SIAM PUBLICATIONS
- DOI
- 10.1137/070690638
- ISSN
- 0036-1410
- eISSN
- 1095-7154
- Number of pages
- 18
- Language
- English
- Date published
- 01/01/2008
- Academic Unit
- Mathematics
- Record Identifier
- 9984240870302771
Metrics
2 Record Views