An equation for the limit state of a superconductor with pinning sites

Abstract

We study the limit state of the inhomogeneous Ginzburg-Landau model as the Ginzburg-Landau parameter k = 1/∈ → ∞, and derive an equation to describe the limit state. We analyze the properties of solutions of the limit equation, and investigate the convergence of (local) minimizers of the Ginzburg-Landau energy with large k. Our results verify the pinning effect of an inhomogeneous superconductor with large k.