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: firstname.lastname@example.org
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
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