We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-10,
author = {Takayoshi Ogawa},
title = {Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {161-184},
zbl = {1133.35020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-10}
}
Takayoshi Ogawa. Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type. Banach Center Publications, Tome 72 (2006) pp. 161-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-10/