A Variational Problem Related to the Ginzburg--Landau Model of Superconductivity with Normal Impurity Inclusion
Shijin Ding, Zuhan Liu, Wanghui Yu · SIAM Journal on Mathematical Analysis · 1998
A variational problem related to the Ginzburg--Landau model of superconductivity with normal impurity inclusion is considered. A standing feature of this problem is the vortex-pinning effect (i.e., the zeros of solutions are attracted to the region occupied by the normal impurities) as some parameters are sufficiently small. Asymptotic behaviors of the solutions of this problem as these parameters tend to zero is studied, and the vortex-pinning effect is proved.