Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data

Piotr Biler, and Jacek Zienkiewicz. "Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data." Bulletin of the Polish Academy of Sciences. Mathematics 63.1 (2015): 41-51. <http://eudml.org/doc/281224>.

@article{PiotrBiler2015,
abstract = {A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.},
author = {Piotr Biler, Jacek Zienkiewicz},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {chemotaxis; blow-up of solutions},
language = {eng},
number = {1},
pages = {41-51},
title = {Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data},
url = {http://eudml.org/doc/281224},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Piotr Biler
AU - Jacek Zienkiewicz
TI - Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 1
SP - 41
EP - 51
AB - A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.
LA - eng
KW - chemotaxis; blow-up of solutions
UR - http://eudml.org/doc/281224
ER -