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Critical self-similar collapse of bacterial colonies
Pavel Lushnikov
UNM
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Critical self-similar collapse of bacterial colonies Pavel Lushnikov UNM |
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ABSTRACT Keller-Segel model describes macroscopic behaviour of bacterial colonies. Bacteria secret chemical which attract other bacteria so that they move along chemical gradient. Keller-Segel model is a parabolic-elliptic system of partial differential equations for bacterial density and chemical concentration. If bacterial density exceed critical value then the density blows up in a finite time which corresponds to bacterial aggregation. In two dimensions collapse is critical and qualitatively it shares many common properties with critical collapse of nonlinear Schroedinger equation. However there are also serious differences, in particular because Keller-Segel model is not the Hamiltonian system. The objective of this work is to find out how blow up occurs. The self-similar solutions near blow up point are studied together with time dependence of these solutions and their stability. |