no. 2
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of 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, Volume 53 (2003) no. 2, pp. 565-624.

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.

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.

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, Volume 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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