Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model

It is proved that a two dimensional evolutionary Ginzburg-Landau superconductivity model is an approximation of a corresponding thin plate three dimensional superconductivity model when the thickness of the plate uniformly approaches zero. Some related topics such as existence of weak solutions to the three dimensional variable thickness model and the convergence when the variable thickness tends to zero are discussed. A numerical experiment using the now model is reported.