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nonlocal conditions

Mathematical Modelling of Natural Phenomena (1)

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Global Existence and Boundedness of Solutionsto a Model of Chemotaxis
J. Dyson, R. Villella-Bressan, G. F. Webb
Journal:

Mathematical Modelling of Natural Phenomena / Volume 3 / Issue 7 / 2008

Published online by Cambridge University Press:

23 October 2008, pp. 17-35

Print publication:

2008
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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.