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Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type. (English) Zbl 1227.35097
The authors consider the Cauchy problem for a Keller-Segel system where the principal part is of the fast diffusion type. They construct global weak solutions with small initial data and show the existence of a blow-up solution in 2D. Decay and extinction are studied as well.

MSC:
35B44 Blow-up in context of PDEs
35K59 Quasilinear parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
92C17 Cell movement (chemotaxis, etc.)
35B40 Asymptotic behavior of solutions to PDEs
Keywords:
Cauchy problem
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