Volume 55, Number 4, July-August 2021
|Page(s)||1545 - 1568|
|Published online||29 July 2021|
Maxwell quasi-variational inequalities in superconductivity
Universität Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann-Str. 9, D-45127 Essen, Germany
* Corresponding author: email@example.com
Accepted: 15 June 2021
This paper is devoted to the mathematical modeling and analysis of a hyperbolic Maxwell quasi-variational inequality (QVI) for the Bean-Kim superconductivity model with temperature and magnetic field dependence in the critical current. Our analysis relies on local (resp. global) boundedness and local (resp. global) Lipschitz continuity assumptions on the critical current with respect to the temperature (resp. magnetic field). Emerging from the Euler time discretization, we analyze the corresponding H(curl)-elliptic QVI and prove its existence using a fixed-point argument in combination with techniques from variational inequalities and Maxwell’s equations. Based on the existence result for the H(curl)-elliptic QVI, we examine the stability and convergence of the Euler scheme, which serve as our fundament for the global well-posedness of the governing hyperbolic Maxwell QVI.
Mathematics Subject Classification: 35L85 / 35Q60
Key words: Maxwell quasi-variational inequality / well-posedness / Bean-Kim critical-state model / high-temperature superconductivity
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.