Description

• Title:
  Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
• Creator:
  Cyranka, Jacek
• Description:
  We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodic boundary conditions and a forcing function constant in time is presented as a case study. We establish the existence of a locally attracting fixed point by using rigorous numerics techniques. To prove that the fixed point is, in fact, globally attracting we introduce a technique relying on a construction of an absorbing set, capturing any sufficiently regular initial condition after a finite time. Then the absorbing set is rigorously integrated forward in time to verify that any sufficiently regular initial condition is in the basin of attraction of the fixed point.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 45, No 2 (June 2015); 655 - 697;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.031/7463
• Subject:
  Viscous Burgers equation;
  computer assisted proof;
  fixed point;
  dissipative PDE;
  rigorous numerics;
  Galerkin projection;
  Primary 65M99;
  35B40;
  Secondary 35B41
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.031
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other