MODELING AND ANALYSIS OF A PERIODIC GINZBURG-LANDAU MODEL FOR TYPE-II SUPERCONDUCTORS

A periodic Ginzburg-Landau model for superconductivity is considered. The model has two novel features compared to periodic problems arising in other settings. First, periodicity is defined with respect to a nonorthogonal lattice that is not necessarily aligned with the coordinate axes. Second, the periodicity of the physical variables implies nonstandard, in the context of periodic problems, relations for the primary dependent variables used in the model. Physical assumptions are introduced that form the basis for the model, and then the mathematical model is derived from these assumptions. The model discussed includes, as special cases, periodic Ginzburg-Landau models appearing in the literature. Then the model equations and its solutions are analyzed, addressing, among others, questions of existence and regularity. The paper closes with some remarks relevant to the use of the model in conjunction with analytic or numerical approximation methods.