Description

• Title:
  Continuity of attractors for net-shaped thin domains
• Creator:
  Elsken, Thomas
• Description:
  Consider a reaction-diffusion equation $u_t=\triangle u+f(u)$ on a family of net-shaped thin domains $\Omega_\varepsilon$ converging to a one dimensional set as $\varepsilon\downarrow 0$. With suitable growth and dissipativeness conditions on $f$ these equations define global semiflows which have attractors $\mathcal{A}_\varepsilon$. In [Th. Elsken, < i> A reaction-diffusion equation on a net-shaped thin domain< /i> , Studia Math. < b> 165< /b> (2004), 159–199] it has been shown that there is a limit problem which also defines a semiflow having an attractor $\mathcal{A}_0$, and the family of attractors is upper-semi-continuous at $\varepsilon=0$. Here we show that under a stronger dissipativeness condition the family of attractors $\mathcal{A}_\varepsilon$, $\varepsilon\ge 0$, is actually continuous at $\varepsilon=0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2005.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 26, No 2 (December 2005); 315 - 354;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.035/9288
• Subject:
  Reaction-diffusion equations;
  thin net shaped domain;
  continuity of attractors;
  35B41;
  25K20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.035
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other