Asymptotics of parabolic equations with possible blow-up

Volume 99 / 2004

Radosław Czaja 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.

Authors

  • Radosław CzajaInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
    e-mail

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