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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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Keywords: Chemotaxis, Keller-Segel Model, cross diffusion, stationary solutions, bifurcation, global bifurcation, time map, exchange of stability
Article copyright: © Copyright 1985 American Mathematical Society