Description

• Title:
  Attractor for a model of extensible beam with damping on time-dependent space
• Creator:
  Meng, Fengjuan;
  Wang, Yonghai;
  Zhao, Chunxiang
• Description:
  In this paper, we study the asymptotic behavior of the following extensible beam equations: $$ \varepsilon(t) u_{tt}+\Delta^2 u-M\bigg(\int_\Omega |\nabla u|^2dx\bigg) \Delta u +\alpha u_t+\varphi (u)=f, \quad t> \tau, $$ where $\varepsilon(t)$ is a decreasing function of time vanishing at infinity. After generalizing the abstract results on time dependent space, we establish an invariant time-dependent global attractor for the equation by proving the well-posedness (thereby, the existence of process), dissapativity and the compactness of the process. Our work supplements the theoretical results on time-dependent space and the results on the longtime behavior of the model.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 365 - 393;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.037/28143 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.037/28144
• Subject:
  Time-dependent;
  attractors;
  extensible beam equations;
  non-autonomous;
  Primary;
  37L05;
  35B40;
  Secondary;
  35B4
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.037
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other