Recovering Asymptotics at Infinity of Perturbations of Stratified Media

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 $c^2(x,y)\Delta$. The function $c$ is a perturbation of $c_0\left(y\right)$, which is constant for sufficiently large $\left|y\right|$ 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.

Détail

DOI : 10.5802/jedp.566