ASYMPTOTICS FOR SOLUTIONS OF THE GINZBURG-LANDAU EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{\in}$, $A_{\in}$) which minimize the Ginzburg-Landau energy functional $E_{\in}$(u, A). We show that the solutions ( $u_{\in$}$ , $A_{\in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $\in$longrightarrow0.ow0.