Asymptotics of parabolic equations with possible blow-up
Volume 99 / 2004
Colloquium Mathematicum 99 (2004), 61-73
MSC: Primary 35B40; Secondary 35K90, 35K55.
DOI: 10.4064/cm99-1-7
Abstract
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.
