Radially symmetric solutions for a limiting form of the Ginzburg-Landau model (Q2866659)

The author investigates existence and properties of radially symmetric solutions of a semilinear system that is a limiting form of the Ginzburg-Landau model. The problem arises from mathematical theory of superconductivity. A radially symmetric solution of a certain form is sought when the domain is a disk, and the profile of the solution is studied. Existence and regularity of the solution is addressed, and some numerically observed properties are verified rigorously. Estimate of the so-called critical field is obtained for arbitrary values of \(\lambda\) (the penetration depth of the magnetic field), and the critical field is determined as \(\lambda\) approaches zero. Stability analysis and comparable properties of the solution are presented when the domain is an annulus or exterior of a disc.