Abstract
We study the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with some diffusion coefficients being zero. The main tools to obtain our results are comparison principle, suitably constructed super-sub solutions, and squeezing methods. No spectrum analysis of the linear operator associated with traveling front solutions under study is needed. Therefore, our results not only recover and/or complement earlier stability results in the literature, but also provide a simple method to show the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with positive diffusion coefficients.
| Original language | English |
|---|---|
| Pages (from-to) | 601-623 |
| Number of pages | 23 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 21 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2008 Jun |
| Externally published | Yes |
Keywords
- Asymptotic stability
- Bistable
- Exponential stability
- Monotone system
- Reaction-diffusion system
- Traveling front solution
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics