A semi-elliptic system arising in the theory of type-II superconductivity

H. Berestycki, A. Bonnet & S. J. Chapman

A reduced form of the Ginzburg-Landau equations of superconductivity is considered, corresponding to the formal limit as the Ginzburg-Landau parameter $\kappa$ tends to infinity. Existence and uniqueness of the solution is established, up to the point at which the magnitude of the potential first becomes equal to $1/\sqrt{3}$, when the solution becomes linearly unstable. The instability is shown to occur first on the boundary of the sample. Finally a more complete study of one-dimensional and radially-symmetric cases is presented.