Asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions

摘要

In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions $(u_epsilon, A_epsilon)$ which minimize the Ginzburg-Landau energy functional $ E_epsilon (u,A)$. We show that the solutions $(u_epsilon, A_epsilon)$ converge to some $(u_*,A_*)$ in various norms as the coupling parameter $epsilon o 0$.