Description

• Title:
  Inertial manifolds for a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation
• Creator:
  Bonfoh, Ahmed;
  Grasselli, Maurizio;
  Miranville, Alain
• Description:
  We consider a singular perturbation of the generalized viscous Cahn-Hilliard equation based on constitutive equations introduced by M. E. Gurtin and we establish the existence of a family of inertial manifolds which is continuous with respect to the perturbation parameter $\varepsilon> 0$ as $\varepsilon$ goes to 0. In a recent paper, we proved a similar result for the singular perturbation of the standard viscous Cahn-Hilliard equation, applying a construction due to X. Mora and J. Sol\`a-Morales for equations involving linear self-adjoint operators only. Here we extend the result to the singularly perturbed Cahn-Hilliard-Gurtin equation which contains a non-self-adjoint operator. Our method can be applied to a larger class of nonlinear dynamical systems.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 1 (March 2010); 155 - 185;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.010/8463
• Subject:
  Generalized Cahn-Hilliard equations;
  singular perturbations;
  inertial manifolds;
  35B25;
  35B40;
  37L25;
  80C26
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other