The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
The Diffusion Limit of Transport Equations II: Chemotaxis Equations
Abstract
In this paper, we use the diffusion-limit expansion of transport equations developed earlier [T. Hillen and H. G. Othmer, SIAM J. Appl. Math., 61 (2000), pp. 751--775] to study the limiting equation under a variety of external biases imposed on the motion. When applied to chemotaxis or chemokinesis, these biases produce modification of the turning rate, the movement speed, or the preferred direction of movement. Depending on the strength of the bias, it leads to anisotropic diffusion, to a drift term in the flux, or to both, in the parabolic limit. We show that the classical chemotaxis equation---which we call the Patlak--Keller--Segel--Alt (PKSA) equation---arises only when the bias is sufficiently small. Using this general framework, we derive phenomenological models for chemotaxis of flagellated bacteria, of slime molds, and of myxobacteria. We also show that certain results derived earlier for one-dimensional motion can easily be generalized to two- or three-dimensional motion as well.
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Cites
Handbook of Stochastic Methods
Gardiner, C. W. (1983) · Springer Series in Synergetics · doi:10.1007/978-3-662-02377-8 · Cited by 5,961
Initiation of slime mold aggregation viewed as an instability
Keller, E. F., & Segel, L. A. (1970) · Journal of Theoretical Biology · doi:10.1016/0022-5193(70)90092-5 · Cited by 3,662
Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking
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Keller, E. F., & Segel, L. A. (1971) · Journal of Theoretical Biology · doi:10.1016/0022-5193(71)90050-6 · Cited by 1,886
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Random walk with persistence and external bias
Patlak, C. S. (1953) · The Bulletin of Mathematical Biophysics · doi:10.1007/bf02476407 · Cited by 1,008
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Models of dispersal in biological systems
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Self-citationON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION
GOLDSTEIN, S. (1951) · The Quarterly Journal of Mechanics and Applied Mathematics · doi:10.1093/qjmam/4.2.129 · Cited by 751
Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
Stevens, A., & Othmer, H. G. (1997) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139995288976 · Cited by 704
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Cited by
A user’s guide to PDE models for chemotaxis
Hillen, T., & Painter, K. J. (2009) · Journal of Mathematical Biology · doi:10.1007/s00285-008-0201-3 · Cited by 1,650
Self-citationCodling, E. A., Plank, M. J., & Benhamou, S. (2008) · Journal of The Royal Society Interface · doi:10.1098/rsif.2008.0014 · Cited by 1,482
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
Bellomo, N., Bellouquid, A., Tao, Y., & Winkler, M. (2015) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s021820251550044x · Cited by 1,077
ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
BELLOMO, N., LI, N. K., & MAINI, P. K. (2008) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202508002796 · Cited by 420
From Individual to Collective Behavior in Bacterial Chemotaxis
Erban, R., & Othmer, H. G. (2004) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139903433232 · Cited by 279
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Metadata
- Authors
- Othmer, H. G., & Hillen, T.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 2002-01
- Volume
- 62
- Issue
- 4
- Pages
- 1222-1250
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2014527760
- Cited by
- 347
- References
- 25
- FWCI
- 31.19
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
