Vortex Dynamics of Ginzburg–Landau Equations in Inhomogeneous Superconductors

We study a Ginzburg–Landau equation of parabolic type in inhomogeneous superconductors. It is proved that the vortices are attracted by impurities so that they are pinned by inhomogeities in the superconducting materials. This fact was predicted recently by Chapman and Richardson using a method of formal matched asymptotics.