MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.

Feb 24, 2015
Mar 25, 2015
MSC Codes:
35B44, 35M33, 35A01, 35Q92, 92Q17
chemotaxis-growth system, blowup, global solutions, hyperbolic-elliptic system, parabolic-elliptic system

Related publications

2016 Repository Open Access
Kyungkeun Kang and Angela Stevens

Blowup and global solutions in a chemotaxis-growth system

In: SIAM journal on mathematical analysis, 135 (2016), pp. 57-72