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, Volume 36 (2002) no. 3, p. 461-487

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 $-\infty$.

DOI : https://doi.org/10.1051/m2an:2002021
Classification:  35P,  47A70,  47B25,  78A50
Keywords: superconducting transmission lines, wave-guides, self-adjointness, spectral analysis, non elliptic operators
@article{M2AN_2002__36_3_461_0,
author = {Bonnet-Bendhia, Anne-Sophie and Ramdani, Karim},
title = {A non elliptic spectral problem related to the analysis of superconducting micro-strip lines},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {3},
year = {2002},
pages = {461-487},
doi = {10.1051/m2an:2002021},
zbl = {1070.35503},
mrnumber = {1918940},
language = {en},
url = {http://www.numdam.org/item/M2AN_2002__36_3_461_0}
}

Bonnet-Bendhia, Anne-Sophie; 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, Volume 36 (2002) no. 3, pp. 461-487. doi : 10.1051/m2an:2002021. http://www.numdam.org/item/M2AN_2002__36_3_461_0/

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