Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 362, Issue 2, Pages 553-564Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2009.08.012
Keywords
Chemotaxis; Blow-up; Fast diffusion; Global existence; Pattern formation
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In this paper, we study a strongly coupled parabolic system with cross diffusion term which models chemotaxis. The diffusion coefficient goes to infinity when cell density tends to an allowable maximum value. Such 'fast diffusion' leads to global existence of solutions in bounded domains for any given initial data irrespective of the spatial dimension, which is usually the goal of many modifications to the classical Keller-Segel model. The key estimates that make this possible have been obtained by a technique that uses ideas from Moser's iterations. (C) 2009 Elsevier Inc. All rights reserved.
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