## Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis.(English)Zbl 0902.35010

Summary: This paper is concerned with a nonlinear parabolic-elliptic system which is a simplified version of the Keller-Segel model with a sensitivity function $$\phi(s)$$ specified as $$\phi(s)= s^p$$ $$(p>0)$$ or $$\phi(s)= \log s$$. The global existence and blow-up of solutions are studied in radially symmetric situations.

### MSC:

 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) 35B40 Asymptotic behavior of solutions to PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations