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Spectral study of a coupled compact-noncompact problem

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  • Law
  • Musicology
  • Physics

Abstract

Spectral study of a coupled compact-noncompact problem RAIRO MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE A. BENKADDOUR J. SANCHEZ-HUBERT Spectral study of a coupled compact- noncompact problem RAIRO – Modélisation mathématique et analyse numérique, tome 26, no 6 (1992), p. 659-672. <http://www.numdam.org/item?id=M2AN_1992__26_6_659_0> © AFCET, 1992, tous droits réservés. L’accès aux archives de la revue « RAIRO – Modélisation mathématique et analyse numérique » implique l’accord avec les conditions générales d’uti- lisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ J J U > > i MOOÉUSATION MATHEMATIQUE ET ANALYSE NUMÉRIQUE (Vol 26, n° 6, 1992, p 659 à 672) SPECTRAL STUDY OF A COUPLED COMPACT-NONCOMPACT PROBLEM (*) by A. BENKADDOUR (*) and J. SANCHEZ-HUBERT (2) Commumcated by P GEYMONAT Abstract — We consider the coupled problem of acoustic vibration of air in a porous medium Op, made of infinitely close thin sheets, parallel to the plane (xx, x3), in contact withfree air in some région flf We assume that there is no interaction between the sheets unless by the région as The case of a porous medium made ofthin channels parallel to the xx-axis was consider ed in [1, 2,3] In this paper, we consider a somewhat more complicated problem because completely explicit solutions are not avaüable in gênerai Let us dénote by A the operator associated with the coupled eigenvalue problem ( - Au = ü>2u) andbyAp(x2) the operator associated in the sheetx2 = Const in 12p In order to study the spectrum o f A we consider two cases according to the values of co2. In the f ir st case (when (o2 is not an eigenvalue of the problem in Op), the problem reduces to an imphcit eigenvalue problem i

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