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/