On the parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis

Details On the parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis On the parabolic-elliptic limit of the doubly parabolic Keller--Segel system modelling chemotaxis

2008-04-07

arxiv.org/abs/0804.1000v2

Studia Math. 193, 3 (2009) 241--261

Mathematics

Analysis of PDEs

25 pages. Second version revised according to referee's remark. To appear in Studia Math

Scientific paper

We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.

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