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 2004 |
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Keywords
- Bio-reactor model
- Center manifold theorem
- Heteroclinic orbit
- Singular perturbation theory
- Traveling waves
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Applied Mathematics
- Modeling and Simulation
Cite this
Traveling waves in a bio-reactor model. / Smith, Hal; Zhao, Xiao Qiang.
In: Nonlinear Analysis: Real World Applications, Vol. 5, No. 5, 12.2004, p. 895-909.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Traveling waves in a bio-reactor model
AU - Smith, Hal
AU - Zhao, Xiao Qiang
PY - 2004/12
Y1 - 2004/12
N2 - 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.
AB - 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.
KW - Bio-reactor model
KW - Center manifold theorem
KW - Heteroclinic orbit
KW - Singular perturbation theory
KW - Traveling waves
UR - http://www.scopus.com/inward/record.url?scp=4344640995&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=4344640995&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2004.05.001
DO - 10.1016/j.nonrwa.2004.05.001
M3 - Article
AN - SCOPUS:4344640995
VL - 5
SP - 895
EP - 909
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
SN - 1468-1218
IS - 5
ER -