The breakdown of superconductivity in the presence of magnetic steps

Wafaa Assaad

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7 Citations (SciVal)


Many earlier works were devoted to the study of the breakdown of superconductivity in type-II superconducting bounded planar domains, submitted to smooth magnetic fields. In the present contribution, we consider a new situation where the applied magnetic field is piecewise-constant, and the discontinuity jump occurs along a smooth curve meeting the boundary transversely. To handle this situation, we perform a detailed spectral analysis of a new effective model. Consequently, we establish the monotonicity of the transition from a superconducting to a normal state. Moreover, we determine the location of superconductivity in the sample just before it disappears completely. Interestingly, the study shows similarities with the case of corner domains subjected to constant fields.

Original languageEnglish
Article number2050005
JournalCommunications in Contemporary Mathematics
Issue number2
Early online date2020 Mar 4
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Mathematics


  • diamagnetic inequality
  • Ginzburg-Landau equations
  • magnetic Laplacian
  • step magnetic fields


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