Jäger, W.; Luckhaus, S. On explosions of solutions to a system of partial differential equations modelling chemotaxis. (English) Zbl 0746.35002 Trans. Am. Math. Soc. 329, No. 2, 819-824 (1992). 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) Cited in 9 ReviewsCited in 499 Documents 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) Keywords:radially symmetric solution; dynamic behaviour; global existence of smooth solutions; explosion of bacteria concentration in finite time; Keller-Segel model; chemotactic aggregation × Cite Format Result Cite Review PDF Full Text: DOI