Giorgi, T.; Phillips, D. The breakdown of superconductivity due to strong fields for the Ginzburg–Landau model. (English) Zbl 0920.35058 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 \(\bar h=O(\kappa)\). Cited in 51 Documents 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 PDF BibTeX XML Cite \textit{T. Giorgi} and \textit{D. Phillips}, SIAM J. Math. Anal. 30, No. 2, 341--359 (1999; Zbl 0920.35058) Full Text: DOI