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A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-02-27
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
This paper deals with a Neumann boundary value problem for a Keller-Segel model with a cubic source term in a d-dimensional box (d=1,2,3), which describes the movement of cells in response to the presence of a chemical signal substance.
It is proved that, given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(1/δ).
Each initial perturbation certainly can behave drastically differently from another, which gives rise to the richness of patterns.
Our results provide a mathematical description for early pattern formation in the model.
American Psychological Association (APA)
Fu, Shengmao& Liu, Ji. 2013. A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term. Advances in Mathematical Physics،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-509410
Modern Language Association (MLA)
Fu, Shengmao& Liu, Ji. A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term. Advances in Mathematical Physics No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-509410
American Medical Association (AMA)
Fu, Shengmao& Liu, Ji. A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term. Advances in Mathematical Physics. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-509410
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509410