Abstract
The existence of a family of traveling waves is established for a parabolic system modeling single species growth in a plug flow reactor, proving a conjecture of Kennedy and Aris (Bull. Math. Biol. 42 (1980) 397) for a similar system. The proof uses phase plane analysis, geometric singular perturbation theory and the center manifold theorem.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 895-909 |
| Number of pages | 15 |
| Journal | Nonlinear Analysis: Real World Applications |
| Volume | 5 |
| Issue number | 5 |
| DOIs | |
| State | Published - Dec 1 2004 |
Keywords
- Bio-reactor model
- Center manifold theorem
- Heteroclinic orbit
- Singular perturbation theory
- Traveling waves
ASJC Scopus subject areas
- Analysis
- Engineering(all)
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics
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Cite this
Smith, H., & Zhao, X. Q. (2004). Traveling waves in a bio-reactor model. Nonlinear Analysis: Real World Applications, 5(5), 895-909. https://doi.org/10.1016/j.nonrwa.2004.05.001