On the Lawrence–Doniach and Anisotropic Ginzburg–Landau Models for Layered Superconductors

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Abstract
The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to zero, the Lawrence-Doniach model reduces to the anisotropic Ginzburg- Landau model. Finally, simplified versions of the models are derived that can be used to accurately simulate high-temperature superconductors