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Global Existence and Boundedness of Solutionsto a Model of Chemotaxis

Published online by Cambridge University Press:  23 October 2008

J. Dyson ,
R. Villella-Bressan  and
G. F. Webb
J. Dyson
Affiliation:
Mansfield College, University of Oxford, Oxford, UK
R. Villella-Bressan
Affiliation:
Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padova, Italy
G. F. Webb*
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee
*
janet.dyson@mansfield.ox.ac.uk
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Abstract

A model of chemotaxis is analyzed that prevents blow-up of solutions. The modelconsists of a system of nonlinear partial differential equations for the spatial populationdensity of a species and the spatial concentration of a chemoattractant in n-dimensionalspace. We prove the existence of solutions, which exist globally, and are L∞-bounded onfinite time intervals. The hypotheses require nonlocal conditions on the species-inducedproduction of the chemoattractant.

Keywords

chemotaxisglobal solutionboundednessnonlocal conditionsdiffusionanalytic semigroupfractional power
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 17 - 35
Copyright
© EDP Sciences, 2008

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