The breakdown of superconductivity due to strong fields for the Ginzburg–Landau model. (English) Zbl 0920.35058

Giorgi, T.; Phillips, D.

SIAM J. Math. Anal. 30, No. 2, 341-359 (1999).

Summary: We study the behavior of a superconducting material subjected to a constant applied magnetic field, \(H_a=he\) with \(| b| =1\), using the Ginzburg-Landau theory. We analytically show the existence of a critical field \(\bar h,\) for which when \(h>\bar h,\) the normal states are the only solutions to the Ginzburg–Landau equations. We estimate \(\bar h\). As \(\kappa\downarrow 0\) we derive \(\bar h=O(1)\), while as \(\kappa\to\infty\) we obtain \(\bar h=O(\kappa)\).

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35Q40	PDEs in connection with quantum mechanics

Keywords:

Ginzburg-Landau equations; upper critical fields; normal state