✦ LIBER ✦

Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity

✍ Scribed by Michael Winkler

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 123 KB
Volume: 283
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200810838

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✦ Synopsis

Abstract

We consider the chemotaxis system

equation image

under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ ℝ^n^. The chemotactic sensitivity function is assumed to generalize the prototype

equation image

It is proved that no chemotactic collapse occurs in the sense that for any choice of nonnegative initial data (with some r > n), the corresponding initial‐boundary value problem possesses a unique global solution that is uniformly bounded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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