Description

• Title:
  Upper semicontinuity of global attractors for the perturbed viscous Cahn-Hilliard equations
• Creator:
  Kania, Maria B.
• Description:
  It is known that the semigroup generated by the initial-boundary value problem for the perturbed viscous Cahn-Hilliard equation with $\varepsilon> 0$ as a parameter admits a global attractor $\mathcal{A}_{\varepsilon}$ in the phase space $X^{{1}/{2}} =(H^2(\Omega)\cap H^{1}_{0}(\Omega))\times L^2(\Omega)$, $\Omega\subset \mathbb{R}^n$, $n\leq 3$ (see [M. B. Kania, < i> Global attractor for the perturbed viscous Cahn-Hilliard equation< /i> , Colloq. Math. < b> 109< /b> (2007), 217-229]). In this paper we show that the family $\{\mathcal{A}_{\varepsilon}\}_{\varepsilon\in[0,1]}$ is upper semicontinuous at $0$, which means that the Hausdorff semidistance $$ d_{X^{{1}/{2}}}(\mathcal{A}_{\varepsilon},\mathcal{A}_0)\equiv \sup_{\psi\in \mathcal{A}_{\varepsilon}}\inf_{\phi\in\mathcal{A}_{0}}\| \psi-\phi\|_{X^{{1}/{2}}}, $$ tends to 0 as $\varepsilon\to 0^{+}$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2008.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 32, No 2 (December 2008); 327 - 345;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.051/8799
• Subject:
  Perturbed viscous Cahn-Hilliard equation;
  global attractor;
  upper semicontinuity;
  35B41;
  35L35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.051
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other