On the parabolic-elliptic limit of the doubly parabolic
Keller–Segel system modelling chemotaxis
Studia Mathematica, Tome 193 (2009) no. 3, pp. 241-261
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
establish results convergence strong topologies solutions parabolic parabolic keller segel system plane corresponding solutions parabolic elliptic model physical parameter goes zero main tools suitable space time estimates implying global existence slowly decaying general nonintegrable solutions these models under natural smallness assumption
Affiliations des auteurs :
Piotr Biler 1 ; Lorenzo Brandolese 2
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author = {Piotr Biler and Lorenzo Brandolese},
title = {On the parabolic-elliptic limit of the doubly parabolic
{Keller{\textendash}Segel} system modelling chemotaxis},
journal = {Studia Mathematica},
pages = {241--261},
publisher = {mathdoc},
volume = {193},
number = {3},
year = {2009},
doi = {10.4064/sm193-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm193-3-2/}
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%0 Journal Article %A Piotr Biler %A Lorenzo Brandolese %T On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis %J Studia Mathematica %D 2009 %P 241-261 %V 193 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm193-3-2/ %R 10.4064/sm193-3-2 %G en %F 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 193 (2009) no. 3, pp. 241-261. doi: 10.4064/sm193-3-2
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