Ginzburg-landau equation and stable steady state solutions in a non-trivial domain
Shuichi Jimbo, Yoshihisa Morita, Jian Zhai · Communications in Partial Differential Equations · 1995
The Ginzburg-Landau equation with a large parameter is studied in a bounded domain with the Neumann B.C. It is shown that many kinds of stable non-constant solutions exist in domains with some topological condition. If the space dimension is 2 or 3 and if the domain is not simply connected, this condition holds.