Description

• Title:
  Existence, uniqueness and properties of global weak solutions to interdiffusion with Vegard rule
• Creator:
  Sapa, Lucjan;
  Bożek, Bogusław;
  Danielewski, Marek
• Description:
  We consider the diffusional transport in an $r$-component solid solution. The model is expressed by the nonlinear system of strongly coupled parabolic differential equations with initial and nonlinear boundary conditions. The techniques involved are the local mass conservation law for fluxes, which are a sum of the diffusional and Darken drift terms, and the Vegard rule. The considered boundary conditions allow the physical system to be not only closed but also open. The theorems on existence, uniqueness and properties of global weak solutions are proved. The main tool used in the proof of the existence result is the Galerkin approximation method. The agreement between the theoretical results, numerical simulations and experimental data is shown.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.07.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 2 (December 2018); 423 - 448;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.008/15160 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.008/15161
• Subject:
  Interdiffusion;
  Darken method;
  Vegard rule;
  parabolic nonlinear system;
  existence;
  uniqueness;
  properties of global weak solutions;
  Galerkin approximation;
  Primary;
  35K61;
  35K51;
  35D30;
  35Q70;
  Secondary;
  35A01;
  35A02;
  35A35;
  65N30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.008
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other