# A spectral study of an infinite axisymmetric elastic layer

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topChorfi, 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

top- A. Bamberger, Y. Dermenjian and P. Joly, Mathematical analysis of the propagation of elastic guided waves in heterogeneous media. J. Differential Equations88 (1990) 113-154. Zbl0714.35045
- A. Bamberger, P. Joly and M. Kern, Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section. RAIRO Modél. Math. Anal. Numér.25 (1991) 1-30. Zbl0739.73009
- M. Bouchon and D.P. Schmitt, Full-wave acoustic logging in an irregular borehole. Geophysics54 (1989) 758-765.
- L. Chorfi, Étude mathématique des modes guidés dans un milieu élastique à symétrie de révolution. RAIRO Modél. Math. Anal. Numér.30 (1996) 299-342.
- D.J. Duterte, A.S. Bonnet-Ben Dhia and P. Joly, Mathematical analysis of elastic surface waves in topographic waveguides. M 3AS (Math. Models Methods Appl. Sci.)9 (1999) 755-798. Zbl0946.74034
- G. Duvaut, Mécanique des milieux continus. Masson, Paris (1990).
- T. Kato, Perturbation Theory for Linear Operators. 2nd edn., Springer-Verlag, New York (1976). Zbl0342.47009
- J. Miklowitz, The Theory of Elastic Waves and Wave Guides. North-Holland Publishing Company, Amsterdam, New York, Oxford (1980). Zbl0565.73025
- J.A. Nitsche, On Korn's second inequality. RAIRO Anal. Numér.15 (1981) 237-248. Zbl0467.35019
- 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
- M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV Analysis of Operators. Academic Press, New York, San Francisco, London (1978). Zbl0401.47001
- M. Schechter, Operator Methods in Quantum Mechanics. North-Holland Publishing Company, Amsterdam, New York, Oxford (1981). Zbl0456.47012
- G. A. Winbow, Seismic sources in open cased boreholes. Geophysics56 (1991) 1040-1050.

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