Description

• Title:
  Parabolic equations with critical nonlinearities
• Creator:
  Cholewa, Jan W.;
  Dłotko, Tomasz
• Description:
  As well known the problem of global continuation of solutions to semilinear parabolic equations is completely solved when the nonlinear term is subordinated to an $\alpha$-power of the main linear operator with $\alpha\in[0,1)$. In this paper we study three examples of {\it critical problems} in which the mentioned subordination takes place with $\alpha=1$, i.e. the nonlinearity has the same {\it order of magnitude} as the linear main part. We use specific techniques of proving global solvability that fit well the considered examples for which general abstract methods fail.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 21, No 2 (June 2003); 311 - 324;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.019/9606
• Subject:
  Global solutions;
  critical nonlinearity;
  Navier-Stokes system;
  35K55;
  35K90;
  35B60;
  35Q30;
  35G30;
  35B35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.019
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other