Description

• Title:
  Characterization of the limit of some higher dimensional thin domain problems
• Creator:
  Elsken, Thomas;
  Prizzi, Martino
• Description:
  A reaction-diffusion equation on a family of three dimensional thin domains, collapsing onto a two dimensional subspace, is considered. In [< i> The effect of domain squeezing upon the dynamics of reaction-diffusion equations< /i> , J. Differential Equations < b> 173< /b> (2001), 271–320] it was proved that, as the thickness of the domains tends to zero, the solutions of the equations converge in a strong sense to the solutions of an abstract semilinear parabolic equation living in a closed subspace of $H^1$. Also, existence and upper semicontinuity of the attractors was proved. In this work, for a specific class of domains, the limit problem is completely characterized as a system of two-dimensional reaction-diffusion equations, coupled by mean of compatibility and balance boundary conditions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2002.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 20, No 1 (September 2002); 151 - 178;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.031/9643
• Subject:
  Reaction-diffusion equations;
  thin domains;
  35K57;
  74G40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.031
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other