Description

• Title:
  Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux
• Creator:
  Burczak, Jan;
  Granero-Belinchon, Rafael
• Description:
  A semilinear version of parabolic-elliptic Keller--Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutions under very general conditions on our semilinearity. It can degenerate, but has to provide a stronger dissipation for large values of a solution than in the critical linear case or we need to assume certain (explicit) data smallness. Moreover, when one considers a~logistic term with a parameter $r$, we obtain our results even for diffusions slightly weaker than the critical linear one and for arbitrarily large initial datum, provided $r\ge 1$. For a mild logistic dampening, we can improve the smallness condition on the initial datum up to $\sim {1}/({1-r})$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 1 (March 2016); 369 - 387;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.012/7790 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.012/7791
• Subject:
  Fractional Keller-Segel;
  critical dissipation;
  bounded solutions;
  logistic dampening;
  Primary;
  35455;
  Secondary;
  35B41;
  92C17
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.012
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other