The Vortex Dynamics of a Ginzburg-landau System under Pinning Effect

We study the vortex dynamical behaviour of a Ginzburg-Landau (G-L) system of related to inhomogeneous superconductors as well as to three-dimensional superconducting thin films having variable thickness. It is proved that the vortices are attracted by impurities or inhomogeities in the superconducting materials. This rigorously verifies the fact predicted recently by a few authors using a method of formal asymptotics or approxiamate computation. Using this fact, furthermore, we prove the strong H-convergence of the solutions to the G-L system.