A spectral study of an infinite axisymmetric elastic layer
Chorfi, Lahcène
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001), p. 849-863 / Harvested from Numdam
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Nous présentons ici une étude théorique des modes propres dans une couche élastique axisymétrique. La modélisation mathématique permet de ramener ce problème à l’étude spectrale d’une suite d’opérateurs A n , n∈ℕ, non bornés et autoadjoints dans un espace de Hilbert adéquat. On montre que le spectre essentiel de A n est un intervalle du type [γ,+∞[ et que, sous certaines conditions portant sur les coefficients du milieu, le spectre discret est non vide.

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 A n , n∈ℕ, in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [γ,+∞[ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

Publié le : 2001-01-01
Classification:  35P15,  47A70,  73D30 
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     author = {Chorfi, Lahc\`ene},
     title = {A spectral study of an infinite axisymmetric elastic layer},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {35},
     year = {2001},
     pages = {849-863},
     mrnumber = {1866270},
     zbl = {0994.35100},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2001__35_5_849_0}
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Chorfi, Lahcène. A spectral study of an infinite axisymmetric elastic layer. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 849-863. http://gdmltest.u-ga.fr/item/M2AN_2001__35_5_849_0/

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