Journal article
Exponential stability of large-amplitude traveling fronts for quasi-linear relaxation systems with diffusion
Physica. D, Vol.240(11), pp.971-983
2011
DOI: 10.1016/j.physd.2011.02.003
Abstract
This paper is concerned with the stability of traveling front solutions for 2×2 quasi-linear relaxation systems with small diffusion rate. By applying geometric singular perturbation method, special Evans function estimates, detailed spectral analysis and
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semigroup theories, we prove that all the non-degenerate waves for semi-linear relaxation systems are locally exponentially stable in some exponentially weighted spaces. We also obtain the linear exponential stability of the non-degenerate waves for quasi-linear relaxation systems, where the wave strengths can be large.
► We study 2×2 quasi-linear relaxation systems with small diffusion rate. ► The main interest is the stability of large-amplitude non-degenerate waves. ► For some quasilinear cases the waves are shown linearly exponentially stable. ► For semilinear cases all the waves are shown nonlinearly exponentially stable. ► The existence and approximation of the wave fronts are also obtained.
Details
- Title: Subtitle
- Exponential stability of large-amplitude traveling fronts for quasi-linear relaxation systems with diffusion
- Creators
- Lina Wang - Capital Normal UniversityYaping Wu - Capital Normal UniversityTong Li - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Physica. D, Vol.240(11), pp.971-983
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.physd.2011.02.003
- ISSN
- 0167-2789
- eISSN
- 1872-8022
- Language
- English
- Date published
- 2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984241050902771
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