In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-7,
author = {Tomasz Cie\'slak},
title = {The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {127-132},
zbl = {1103.92007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-7}
}
Tomasz Cieślak. The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below. Banach Center Publications, Tome 72 (2006) pp. 127-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-7/