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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stationary solutions of chemotaxis systems


Author: Renate Schaaf
Journal: Trans. Amer. Math. Soc. 292 (1985), 531-556
MSC: Primary 35B32; Secondary 92A09
MathSciNet review: 808736
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Abstract: The Keller-Segel Model is a system of partial differential equations modelling a mutual attraction of amoebae caused by releasing a chemical substance (Chemotaxis). This paper analyzes the stationary solutions of the system with general nonlinearities via bifurcation techniques and gives a criterion for bifurcation of stable nonhomogeneous aggregation patterns. Examples are discussed with various kinds of nonlinearities modelling the sensitivity of the chemotaxis response.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808736-1
PII: S 0002-9947(1985)0808736-1
Keywords: Chemotaxis, Keller-Segel Model, cross diffusion, stationary solutions, bifurcation, global bifurcation, time map, exchange of stability
Article copyright: © Copyright 1985 American Mathematical Society