Recovering Asymptotics at Infinity of Perturbations of Stratified Media

Tanya Christiansen; Mark S. Joshi

Journées équations aux dérivées partielles (2000)

  • page 1-9
  • ISSN: 0752-0360

Abstract

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We consider perturbations of a stratified medium ℝ x n - 1 × 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.

How to cite

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Christiansen, Tanya, and Joshi, Mark S.. "Recovering Asymptotics at Infinity of Perturbations of Stratified Media." Journées équations aux dérivées partielles (2000): 1-9. <http://eudml.org/doc/93399>.

@article{Christiansen2000,
abstract = {We consider perturbations of a stratified medium $\mathbb \{R\}^\{n-1\}_x\times \mathbb \{R\}_y$, where the operator studied is $c^2(x,y) \Delta $. 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.},
author = {Christiansen, Tanya, Joshi, Mark S.},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-9},
publisher = {Université de Nantes},
title = {Recovering Asymptotics at Infinity of Perturbations of Stratified Media},
url = {http://eudml.org/doc/93399},
year = {2000},
}

TY - JOUR
AU - Christiansen, Tanya
AU - Joshi, Mark S.
TI - Recovering Asymptotics at Infinity of Perturbations of Stratified Media
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 9
AB - We consider perturbations of a stratified medium $\mathbb {R}^{n-1}_x\times \mathbb {R}_y$, where the operator studied is $c^2(x,y) \Delta $. 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.
LA - eng
UR - http://eudml.org/doc/93399
ER -

References

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