Recovering Asymptotics at Infinity of Perturbations of Stratified Media

Christiansen, Tanya; Joshi, Mark S.

Christiansen, Tanya ; Joshi, Mark S.

Journées équations aux dérivées partielles (2000), article no. 2, 9 p.

Résumé

We consider perturbations of a stratified medium $ℝ_{x}^{n - 1} \times ℝ_{y}$ , where the operator studied is $c^{2} (x, y) Δ$ . The function $c$ is a perturbation of $c_{0} (y)$ , which is constant for sufficiently large $| y |$ and satisfies some other conditions. Under certain restrictions on the perturbation $c$ , we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of $c$ from knowledge of $c_{0}$ and the singularities of the scattering matrix at fixed energy.

MR Zbl | 1 citation dans Numdam

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     author = {Christiansen, Tanya and Joshi, Mark S.},
     title = {Recovering {Asymptotics} at {Infinity} of {Perturbations} of {Stratified} {Media}},
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     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     publisher = {Universit\'e de Nantes},
     year = {2000},
     mrnumber = {2001g:35261},
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Christiansen, Tanya; Joshi, Mark S. Recovering Asymptotics at Infinity of Perturbations of Stratified Media. Journées équations aux dérivées partielles (2000), article  no. 2, 9 p. https://www.numdam.org/item/JEDP_2000____A2_0/

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