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1 results

  • A non elliptic spectral problem related to the analysisof superconducting micro-strip lines

  • Anne-Sophie Bonnet-Bendhia, Karim Ramdani
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 36 / Issue 3 / May 2002
    Published online by Cambridge University Press:
    15 August 2002, pp. 461-487
    Print publication:
    May 2002

  • This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines.Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization ofits positive eigenvalues is given. Thanks to this characterization, some conditions on the geometrical (large width) and physical (large dielectric permittivityin modulus) properties of the strip that ensure the existence of positive eigenvalues are derived. Finally, we analyze the asymptotic behavior of the eigenvaluesof A as the dielectric permittivity of the strip goes to -∞.