We establish new results on convergence, in strong topologies, of 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-2,
author = {Piotr Biler and Lorenzo Brandolese},
title = {On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {241-261},
zbl = {1167.35316},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-2}
}
Piotr Biler; Lorenzo Brandolese. On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis. Studia Mathematica, Tome 192 (2009) pp. 241-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-2/