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

Nagai, Toshitaka; Senba, Takasi

Adv. Math. Sci. Appl. 8, No. 1, 145-156 (1998).

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

Keywords:

simplified version of the Keller-Segel model; sensitivity function