A non elliptic spectral problem related to the analysis of superconducting micro-strip lines
Laboratoire SMP, ENSTA, URA 853 du CNRS,
32 Boulevard Victor, 75739 Paris Cedex 15, France. firstname.lastname@example.org.
2 Projet CORIDA, INRIA Lorraine, Campus Scientifique, BP 239, 54506 Vandœuvre-les-Nancy, France. email@example.com.
Revised: 25 February 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 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 -∞.
Mathematics Subject Classification: 35P / 47A70 / 47B25 / 78A50
Key words: Superconducting transmission lines / wave-guides / self-adjointness / spectral analysis / non elliptic operators.
© EDP Sciences, SMAI, 2002