A perturbative method for the spectral analysis of an acoustic multistratified strip

Croc, Elisabeth; Dermenjian, Yves

doi:10.1002/(sici)1099-1476(199812)21:18<1681::aid-mma16>3.3.co;2-w

Cited by 3 publications

(3 citation statements)

References 10 publications

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“…His method was then improved [2,33,37,43] and applied to many other wave propagation phenomena. The scalar wave equation has been intensively studied in numerous situations, for example, perturbed cylindrical waveguides [16,17,29], wedge-shaped regions [18], stratified media [11,13,41] and periodic waveguides [30]. Similar approaches were developed in elastodynamics [10,12,31,34] and electromagnetism [4,41] and for more abstract models [40].…”

Section: Hazard and F Loretmentioning

confidence: 99%

Generalized eigenfunction expansions for conservative scattering problems with an application to water waves

Hazard¹,

Loret²

2007

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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This paper is devoted to a spectral description of wave propagation phenomena in conservative unbounded media, or, more precisely, the fact that a time-dependent wave can often be represented by a continuous superposition of time-harmonic waves. We are concerned here with the question of the perturbation of such a generalized eigenfunction expansion in the context of scattering problems: if such a property holds for a free situation, i.e. an unperturbed propagative medium, what does it become under perturbation, i.e. in the presence of scatterers? The question has been widely studied in many particular situations. The aim of this paper is to collect some of them in an abstract framework and exhibit sufficient conditions for a perturbation result. We investigate the physical meaning of these conditions which essentially consist in, on the one hand, a stable limiting absorption principle for the free problem, and on the other hand, a compactness (or short-range) property of the perturbed problem. This approach is illustrated by the scattering of linear water waves by a floating body. The above properties are obtained with the help of integral representations, which allow us to deduce the asymptotic behaviour of time-harmonic waves from that of the Green function of the free problem. The results are not new: the main improvement lies in the structure of the proof, which clearly distinguishes the properties related to the free problem from those which involve the perturbation.

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Section: Hazard and F Loretmentioning

confidence: 99%

Generalized eigenfunction expansions for conservative scattering problems with an application to water waves

Hazard¹,

Loret²

2007

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…Concerning the existence of the outgoing Green operator, we refer to the papers [3][4][5] by Croc and Dermenjian in the two dimensional case for the operator L c · := div(c 2 grad·) + k 2…”

Section: Remark 13mentioning

confidence: 99%

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

Ikehata¹,

Makrakis²,

Nakamura³

2001

Inverse Problems in Underwater Acoustics

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“…[10] et [6] pour la méthode de l'opérateur conjugué). Par contre, il n'y a que peu de résultats pour des opérateurs qui, dans un certain sens, correspondent aux milieux bistratifiés (voir [8] pour une méthode basée sur les fonctions propres généralisées et [11] pour la méthode de l'opérateur conjugué).…”

Section: (B) Les éLéments De a P (H)\i(h} Sont Des Valeurs Propres Deunclassified

Méthodes à $N$ Corps pour un Problème de Milieux Pluristratifiés Perturbés

Dermenjian¹,

Iftimie²

1999

Publ. Res. Inst. Math. Sci.

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A perturbative method for the spectral analysis of an acoustic multistratified strip

Cited by 3 publications

References 10 publications

Generalized eigenfunction expansions for conservative scattering problems with an application to water waves

Generalized eigenfunction expansions for conservative scattering problems with an application to water waves

Inverse Boundary-Value Problem for Ocean Acoustics Using Point Sources

Méthodes à $N$ Corps pour un Problème de Milieux Pluristratifiés Perturbés

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