Existence, uniqueness and properties of global weak solutions to interdiffusion with Vegard rule
type: Item
instance of: scholarly article
title: Existence, uniqueness and properties of global weak solutions to interdiffusion with Vegard rule
zbMATH Open document ID: 1412.35188
DOI: 10.12775/TMNA.2018.008
author: Lucjan Sapa
author: Bogusław Bożek
author: Marek Danielewski
published in: Topological Methods in Nonlinear Analysis
publication date: 2019-05-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tmna/1532484289
review text: The paper deals with the model for the diffuse mass transport given by the one-dimensional nonlinear system of strongly coupled parabolic differential equations \[ \partial_t\varrho_i=\partial_x\left(\Theta_i(\varrho_1,\dots,\varrho_r)\partial_x\varrho_i-\varrho_i\displaystyle\sum_{j=1}^r\displaystyle\frac{\Omega_j\Theta_j(\varrho_1,\dots,\varrho_r)}{M_j}\partial_x\varrho_j-K(t)\varrho_i\right), \] for $i=1,\dots,r$, $\varrho_i=M_ic_i$, with initial and nonlinear coupled boundary conditions. This equation is obtained from the local mass conservation law for fluxes given by a sum of the diffusional and Darken drift terms, and the Vegard rule. The authors prove the existence, uniqueness, nonnegativity and estimates of the global in time weak solutions in suitable Sobolev spaces for the above problem. Some examples of physical problems and numerical experiments are finally presented.
Mathematics Subject Classification ID: 35K61
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35Q70
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 7051675
zbMATH Keywords: interdiffusion
zbMATH Keywords: Darken method
zbMATH Keywords: Vegard rule
zbMATH Keywords: parabolic nonlinear system
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: properties of global weak solutions
zbMATH Keywords: Galerkin approximation
reviewed by: Rodica Luca
MaRDI profile type: Publication
cites work: Q5318420
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Wikidata QID: Q129545284
description: scientific article; zbMATH DE number 7051675