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

Piotr Biler, and Lorenzo Brandolese. "On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis." Studia Mathematica 193.3 (2009): 241-261. <http://eudml.org/doc/284649>.

@article{PiotrBiler2009,
abstract = {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.},
author = {Piotr Biler, Lorenzo Brandolese},
journal = {Studia Mathematica},
keywords = {Keller–Segel model; chemotaxis; global in time solutions; decay of solutions; blowup of solutions; parabolic-parabolic system; parabolic-elliptic system; space-time estimates},
language = {eng},
number = {3},
pages = {241-261},
title = {On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis},
url = {http://eudml.org/doc/284649},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Piotr Biler
AU - Lorenzo Brandolese
TI - On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 3
SP - 241
EP - 261
AB - 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.
LA - eng
KW - Keller–Segel model; chemotaxis; global in time solutions; decay of solutions; blowup of solutions; parabolic-parabolic system; parabolic-elliptic system; space-time estimates
UR - http://eudml.org/doc/284649
ER -