The regularizing rate of solutions to the Keller-Segel equations in the whole space is estimated just as for the heat equation. As an application of these rate estimates, it is proved that the solution is analytic in spatial variables. Spatial analyticity implies that the propagation speed is infinite, i.e., the support of the solution coincides with the whole space for any short time, even if the support of the initial datum is compact.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-25,
author = {Okihiro Sawada},
title = {On the spatial analyticity of solutions to the Keller-Segel equations},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {421-431},
zbl = {1154.35432},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-25}
}
Okihiro Sawada. On the spatial analyticity of solutions to the Keller-Segel equations. Banach Center Publications, Tome 83 (2008) pp. 421-431. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-25/