We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-9,
author = {Piotr Biler and Lorenzo Brandolese},
title = {Global existence versus blow up for some models of interacting particles},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {293-303},
zbl = {1116.35015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-9}
}
Piotr Biler; Lorenzo Brandolese. Global existence versus blow up for some models of interacting particles. Colloquium Mathematicae, Tome 106 (2006) pp. 293-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-9/