We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-7,
author = {Rados\l aw Czaja},
title = {Asymptotics of parabolic equations with possible blow-up},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {61-73},
zbl = {1058.35137},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-7}
}
Radosław Czaja. Asymptotics of parabolic equations with possible blow-up. Colloquium Mathematicae, Tome 100 (2004) pp. 61-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-7/