Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T04:03:51.752Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

Abstract

A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production 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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)