Nonlinear Diffusion for Bacterial Traveling Wave Phenomenon

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The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher-KPP equation. For this reason, the Keller-Segel equations are widely used for bacterial waves. Note that the Keller-Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.
Publisher
SPRINGER
Issue Date
2023-05
Language
English
Article Type
Article
Citation

BULLETIN OF MATHEMATICAL BIOLOGY, v.85, no.5

ISSN
0092-8240
DOI
10.1007/s11538-023-01138-3
URI
http://hdl.handle.net/10203/306075
Appears in Collection
MA-Journal Papers(저널논문)
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