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

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
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