Macroscopic Models for Superconductivity
- 1 December 1992
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Review
- Vol. 34 (4) , 529-560
- https://doi.org/10.1137/1034114
Abstract
This paper reviews the derivation of some macroscopic models for superconductivity and also some of the mathematical challenges posed by these models. The paper begins by exploring certain analogies between phase changes in superconductors and those in solidification and melting. However, it is soon found that there are severe limitations on the range of validity of these analogies and outside this range many interesting open questions can be posed about the solutions to the macroscopic modelsKeywords
This publication has 30 references indexed in Scilit:
- A free boundary problem arising in electrophotographyNonlinear Analysis, 1991
- Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperatureEuropean Journal of Applied Mathematics, 1990
- The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic LimitsIMA Journal of Applied Mathematics, 1990
- Modelling mushy regionsFlow, Turbulence and Combustion, 1987
- SINGULARITY DEVELOPMENT IN MOVING-BOUNDARY PROBLEMSThe Quarterly Journal of Mechanics and Applied Mathematics, 1985
- Évolution d’une interface par capillarité et diffusion de volume I. Existence locale en tempsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 1984
- On the numerical solution of an alloy solidification problemInternational Journal of Heat and Mass Transfer, 1979
- Propagation of a Magnetic Field into a SuperconductorPhysical Review B, 1958
- Theory of SuperconductivityPhysical Review B, 1957
- Ein neuer Effekt bei Eintritt der Supraleitf higkeitThe Science of Nature, 1933