The Ginzburg--Landau equation: Posed in a quarter-plane
Several existence and uniqueness theorems are stated for the Ginzburg- Landau (GL) equation. First, one extends the global existence theorem for the Cauchy problem of the GL equation on a bounded domain to a theorem on an unbounded domain by using a semigroup technique. In the case of the GL equation in a quarter-plane, one proves a local existence-uniqueness theorem for the classical solution and gives a criterion of small initial-boundary data. Finally, it is shown that, for some special values of the parameters, this local solution is also a global solution.
scientific article; zbMATH DE number 399081