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arXiv: 0804.1000

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

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v2 (2009-03-09)

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

Piotr Biler (  Corresponding author ) 1, Lorenzo Brandolese (  Corresponding author ) 2

(2009)

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.

1:	Instytut Matematyczny
	Uniwersytet Wroclawski
2:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon

Subject

:

Mathematics/Analysis of PDEs Life Sciences/Cellular Biology/Cell Behavior

Keyword(s): chemotaxis system – local and global in time solutions – convergence of solutions – Patlak-Keller-Segel – asymptotic analysis – parabolic-parabolic

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From: Lorenzo Brandolese <>

Submitted on: Monday, 9 March 2009 14:41:39

Updated on: Thursday, 17 March 2011 20:10:43