The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-1,
author = {Andrzej Raczy\'nski},
title = {Weak-$L^{p}$ solutions for a model of self-gravitating particles with an external potential},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {199-216},
zbl = {1113.35030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-1}
}
Andrzej Raczyński. Weak-$L^{p}$ solutions for a model of self-gravitating particles with an external potential. Studia Mathematica, Tome 178 (2007) pp. 199-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-3-1/