Non-minimizing solutions of the Ginzburg-Landau equation

Abstract

Throughout this chapter, we analyze the behavior as $\varepsilon \to 0$ of solutions v_ε of the Ginzburg-Landau equation:

$$ - \Delta {v_\varepsilon } = \frac{1}{{{\varepsilon ^2}}}{v_\varepsilon }\left( {1 - {{\left| {{v_\varepsilon }} \right|}^2}} \right)\quad in G $$

((1))

,

$$ {v_\varepsilon } = g\quad on\,\partial G $$

(2)

.