Geodesic
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
J. Dyson1 ; R. Villella-Bressan2 ; G. F. Webb3
1 Mansfield College, University of Oxford, Oxford, UK
2 Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padova, Italy
3 Department of Mathematics, Vanderbilt University, Nashville, Tennessee
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 17-35

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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.
DOI : 10.1051/mmnp:2008039

J. Dyson 1 ; R. Villella-Bressan 2 ; G. F. Webb 3

1 Mansfield College, University of Oxford, Oxford, UK
2 Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padova, Italy
3 Department of Mathematics, Vanderbilt University, Nashville, Tennessee 
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J. Dyson; R. Villella-Bressan; G. F. Webb. Global Existence and Boundedness of Solutions to a Model of Chemotaxis. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 17-35. doi: 10.1051/mmnp:2008039

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