A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia; Karim Ramdani

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 3, page 461-487
  • ISSN: 0764-583X

Abstract

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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 of its positive eigenvalues is given. Thanks to this characterization, some conditions on the geometrical (large width) and physical (large dielectric permittivity in modulus) properties of the strip that ensure the existence of positive eigenvalues are derived. Finally, we analyze the asymptotic behavior of the eigenvalues of A as the dielectric permittivity of the strip goes to - ∞ .

How to cite

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Bonnet-Bendhia, Anne-Sophie, and Ramdani, Karim. "A non elliptic spectral problem related to the analysis of superconducting micro-strip lines." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.3 (2002): 461-487. <http://eudml.org/doc/244966>.

@article{Bonnet2002,
abstract = {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 $-\infty $. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions on the geometrical (large width) and physical (large dielectric permittivity in modulus) properties of the strip that ensure the existence of positive eigenvalues are derived. Finally, we analyze the asymptotic behavior of the eigenvalues of $A$ as the dielectric permittivity of the strip goes to $-\infty $.},
author = {Bonnet-Bendhia, Anne-Sophie, Ramdani, Karim},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {superconducting transmission lines; wave-guides; self-adjointness; spectral analysis; non elliptic operators},
language = {eng},
number = {3},
pages = {461-487},
publisher = {EDP-Sciences},
title = {A non elliptic spectral problem related to the analysis of superconducting micro-strip lines},
url = {http://eudml.org/doc/244966},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Bonnet-Bendhia, Anne-Sophie
AU - Ramdani, Karim
TI - A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 3
SP - 461
EP - 487
AB - 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 $-\infty $. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions on the geometrical (large width) and physical (large dielectric permittivity in modulus) properties of the strip that ensure the existence of positive eigenvalues are derived. Finally, we analyze the asymptotic behavior of the eigenvalues of $A$ as the dielectric permittivity of the strip goes to $-\infty $.
LA - eng
KW - superconducting transmission lines; wave-guides; self-adjointness; spectral analysis; non elliptic operators
UR - http://eudml.org/doc/244966
ER -

References

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  9. [9] J.G. Ma and I. Wolff, Modeling the Microwave Properties of Superconductors. IEEE Trans. Microwave Theory Tech. 43 (1995) 1053–1059. 
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