A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 5, page 849-863
  • ISSN: 0764-583X

Abstract

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We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, n , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type [ γ , + [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

How to cite

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Chorfi, Lahcène. "A spectral study of an infinite axisymmetric elastic layer." ESAIM: Mathematical Modelling and Numerical Analysis 35.5 (2010): 849-863. <http://eudml.org/doc/197502>.

@article{Chorfi2010,
abstract = { We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, $n\in \mathbb\{N\}$, in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type $[\gamma,+\infty[$ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty. },
author = {Chorfi, Lahcène},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Elasticity; axisymmetry; eigenmodes; min-max principle.; elasticity; axisymmetric layer; waves; spectral theory; eigenvalues; Hilbert spaces},
language = {eng},
month = {3},
number = {5},
pages = {849-863},
publisher = {EDP Sciences},
title = {A spectral study of an infinite axisymmetric elastic layer},
url = {http://eudml.org/doc/197502},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Chorfi, Lahcène
TI - A spectral study of an infinite axisymmetric elastic layer
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 5
SP - 849
EP - 863
AB - We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, $n\in \mathbb{N}$, in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type $[\gamma,+\infty[$ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.
LA - eng
KW - Elasticity; axisymmetry; eigenmodes; min-max principle.; elasticity; axisymmetric layer; waves; spectral theory; eigenvalues; Hilbert spaces
UR - http://eudml.org/doc/197502
ER -

References

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  9. J.A. Nitsche, On Korn's second inequality. RAIRO Anal. Numér.15 (1981) 237-248.  Zbl0467.35019
  10. B. Nkemzi and B. Heinrish, Partial Fourier approximation of the Lamé equation in axisymmetric domains. Math. Methods Appl. Sci.22 (1999) 1017-1041.  Zbl0932.65117
  11. M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV Analysis of Operators. Academic Press, New York, San Francisco, London (1978).  Zbl0401.47001
  12. M. Schechter, Operator Methods in Quantum Mechanics. North-Holland Publishing Company, Amsterdam, New York, Oxford (1981).  Zbl0456.47012
  13. G. A. Winbow, Seismic sources in open cased boreholes. Geophysics56 (1991) 1040-1050.  

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