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Blowup and Global Solutions in a Chemotaxis-Growth System
Kyungkeun Kang and Angela Stevens
We study a Keller-Segel type of system, which includes growth and death of the chemotactic species and an elliptic equation for the chemo-attractant. The problem is considered in bounded domains as well as in the whole space. In case the random motion of the chemotactic species is neglected, a hyperbolic-elliptic problem results, for which we characterize blow-up of solutions in finite time and existence of regular solutions globally in time, in dependence on the systems parameters. For the parabolic-elliptic problem in dimensions three and higher, we establish global existence of regular solutions in a limiting case, which is an extension of the results given by Tello and Winkler in 2007.