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 with smooth boundary 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. In this case, convexity of the domain is needed. 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 (2007).
|Number of pages||16|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2016 Apr 1|
Bibliographical noteFunding Information:
K. Kang was partially supported by NRF - 2014R1A2A1A11051161 and NRF 20151009350 . K. Kang and A. Stevens were partially supported by the Max-Planck-Institute for Mathematics in the Sciences (MPI MIS) , Leipzig. K. Kang thanks Y. Taniuchi for pointing out the result in  to him during a conference at Nara, Japan.
All Science Journal Classification (ASJC) codes
- Applied Mathematics