×

On explosions of solutions to a system of partial differential equations modelling chemotaxis. (English) Zbl 0746.35002

The authors analyzed the Keller-Segel model, which is a system of partial differential equations modeling chemotactic aggregation. They give sufficient conditions for the global existence of smooth solutions. In two space dimensions and radially symmetric situations, explosion of the solution in finite time is shown for a class of initial values.
Reviewer: S.Anita (Iaşi)

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
92C17 Cell movement (chemotaxis, etc.)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B35 Stability in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI