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2018 Existence, uniqueness and properties of global weak solutions to interdiffusion with Vegard rule
Lucjan Sapa, Bogusław Bożek, Marek Danielewski
Topol. Methods Nonlinear Anal. 52(2): 423-448 (2018). DOI: 10.12775/TMNA.2018.008

Abstract

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.

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Lucjan Sapa. Bogusław Bożek. Marek Danielewski. "Existence, uniqueness and properties of global weak solutions to interdiffusion with Vegard rule." Topol. Methods Nonlinear Anal. 52 (2) 423 - 448, 2018. https://doi.org/10.12775/TMNA.2018.008

Information

Published: 2018
First available in Project Euclid: 25 July 2018

zbMATH: 07051675
MathSciNet: MR3915646
Digital Object Identifier: 10.12775/TMNA.2018.008

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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