> Details

Butuzov, Valentin F. [Author]; Nefedov, Nikolai N. [Author]; Recke, Lutz [Author]; Schneider, Klaus R. [Author]

Asymptotics and stability of a periodic solution to a singularly perturbed parabolic problem in case of a double root of the degenerate equation

Reference
management

Bookmarks

Remove from
bookmarks

Share this on Whatsapp

Close

Bookmarks



You can manage bookmarks using lists, please log in to your user account for this.
  • Media type: Text; E-Book; Report
  • Title: Asymptotics and stability of a periodic solution to a singularly perturbed parabolic problem in case of a double root of the degenerate equation
  • Contributor: Butuzov, Valentin F. [Author]; Nefedov, Nikolai N. [Author]; Recke, Lutz [Author]; Schneider, Klaus R. [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2015
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.2141
  • Keywords: singularly perturbed reaction-diffusion equation -- double root of the degenerate equation -- initial boundary value problem -- asymptotic expansion -- asymptotically stable periodic solution -- region of attraction ; 35K57 ; 35B25 ; 35K20 ; 35B10 ; article
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: For a singularly perturbed parabolic problem with Dirichlet conditions we prove the existence of a solution periodic in time and with boundary layers at both ends of the space interval in the case that the degenerate equation has a double root. We construct the corresponding asymptotic expansion in the small parameter. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. We also investigate the stability of this solution and the corresponding region of attraction.