Description

• Title:
  Three-dimensional thermo-visco-elasticity with the Einstein-Debye $(\theta^3+\theta)$-law for the specific heat. Global regular solvability
• Creator:
  Pawłow, Irena;
  Zajączkowski, Wojciech M.
• Description:
  A three-dimensional thermo-visco-elastic system for the Kelvin-Voigt type material at small strain is considered. The system involves the constant heat conductivity and the specific heat satisfying the Einstein-Debye $(\theta^3+\theta)$-law. Such a nonlinear law, relevant at relatively low temperatures, represents the main novelty of the paper. The existence of global regular solutions is proved without the small data assumption. The crucial part of the proof is the strictly positive lower bound on the absolute temperature $\theta$. The problem remains open in the case of the Debye $\theta^3$-law. The existence of local in time solutions is proved by the Banach successive approximations method. The global {\em a priori} estimates are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm. Such estimates allow to extend the local solution step by step in time.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.08.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 1 (September 2018); 161 - 193;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.016/15376 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.016/15377
• Subject:
  Thermo-visco-elastic system;
  Kelvin-Voigt materials;
  Einstein-Debye law for specific heat;
  Sobolev spaces with a mixed norm;
  existence of global regular solutions;
  Primary;
  74B20;
  35K50;
  Secondary;
  35Q71;
  74F05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.016
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other