no. 2
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
[Diffusion dans un milieu stratifié : les propriétés microlocales de la matrice de diffusion et l'obtention du comportement asymptotique des perturbations]
Christiansen, Tanya1 ; Joshi, M. S.2
1 University of Missouri, Department of Mathematics, 201 Math Sciences Bldg, Columbia MO 65211 (USA)
2 Royal Bank of Scotland, Group Risk, Waterhouse Square, 138-142 Holborn, London EC1N 2TH (Grande-Bretagne)
Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 565-624.

On définit la matrice de diffusion dans un milieu stratifié perturbé. Pour une classe de perturbations, on démontre que la partie principale est un opérateur intégral de Fourier sur la sphère à l'infini. On développe un principe d'absorption limite raffiné. Dans de nombreux cas, le symbole de la matrice de diffusion détermine le comportement asymptotique des perturbations.

The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.

DOI : 10.5802/aif.1953
Classification : 35P25, 81U40, 35S30
Keywords: stratified media, scattering matrix, inverse problems, limiting absorption principle
Mot clés : milieu stratifié, matrice de diffusion, problèmes d'inversion, principe d'absorption limite

Christiansen, Tanya 1 ; Joshi, M. S. 2

1 University of Missouri, Department of Mathematics, 201 Math Sciences Bldg, Columbia MO 65211 (USA)
2 Royal Bank of Scotland, Group Risk, Waterhouse Square, 138-142 Holborn, London EC1N 2TH (Grande-Bretagne) 
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Christiansen, Tanya; Joshi, M. S. Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations. Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 565-624. doi : 10.5802/aif.1953. https://aif.centre-mersenne.org/articles/10.5802/aif.1953/

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