1 January 2008
Mathematical Modelling of Natural Phenomena
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.
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