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Currently displaying 1 – 2 of 2

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Recovering the total singularity of a conormal potential from backscattering data

Mark S. Joshi — 1998

Annales de l'institut Fourier

The problem of recovering the singularities of a potential from backscattering data is studied. Let $Ω$ be a smooth precompact domain in $ℝ^{n}$ which is convex (or normally accessible). Suppose $V_{i} = v + w_{i}$ with $v \in C_{c}^{\infty} (ℝ^{n})$ and $w_{i}$ conormal to the boundary of $Ω$ and supported inside $\overline{Ω}$ then if the backscattering data of $V_{1}$ and $V_{2}$ are equal up to smoothing, we show that $w_{1} - w_{2}$ is smooth.

Recovering Asymptotics at Infinity of Perturbations of Stratified Media

Tanya Christiansen; Mark S. Joshi — 2000

Journées équations aux dérivées partielles

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....

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