Description

• Title:
  Rate of convergence of global attractors of some perturbed reaction-diffusion problems
• Creator:
  Arrieta, José M.;
  Bezerra, Flank D. M.;
  Carvalho, Alexandre N.
• Description:
  In this paper we treat the problem of the rate of convergence of attractors of dynamical systems for some autonomous semilinear parabolic problems. We consider a prototype problem, where the diffusion $a_0(\cdot)$ of a reaction-diffusion equation in a bounded domain $\Omega$ is perturbed to $a_\eps(\cdot)$. We show that the equilibria and the local unstable manifolds of the perturbed problem are at a distance given by the order of $\|a_\eps-a_0\|_\infty$. Moreover, the perturbed nonlinear semigroups are at a distance $\|a_\eps-a_0\|_\infty^\theta$ with $\theta< 1$ but arbitrarily close to 1. Nevertheless, we can only prove that the distance of attractors is of order $\|a_\eps-a_0\|_\infty^\beta$ for some $\beta< 1$, which depends on some other parameters of the problem and may be significantly smaller than $1$. We also show how this technique can be applied to other more complicated problems.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2013.04.22
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 41, No 2 (June 2013); 229 - 253;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2013.010/8317
• Subject:
  Attractors;
  continuity;
  uniform exponential attraction;
  rate of convergence\;
  35B41;
  37L30;
  37L45
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2013.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other