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Pré-Publication, Document De Travail Année : 2011

Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems

Résumé

We consider two inverse problems for the multi-channel two-dimensional Schrödinger equation at fixed positive energy, i.e. the equation $-\Delta \psi + V(x)\psi = E \psi$ at fixed positive $E$, where $V$ is a matrix-valued potential. The first is the Gel'fand inverse problem on a bounded domain $D$ at fixed energy and the second is the inverse fixed-energy scattering problem on the whole plane $\R^2$. We present in this paper two algorithms which give efficient approximate solutions to these problems: in particular, in both cases we show that the potential $V$ is reconstructed with Lipschitz stability by these algorithms up to $O(E^{-(m-2)/2})$ in the uniform norm as $E \to +\infty$, under the assumptions that $V$ is $m$-times differentiable in $L^1$, for $m \geq 3$, and has sufficient boundary decay.
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Dates et versions

hal-00594674 , version 1 (20-05-2011)
hal-00594674 , version 2 (24-06-2011)
hal-00594674 , version 3 (08-11-2011)

Identifiants

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Roman Novikov, Matteo Santacesaria. Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems. 2011. ⟨hal-00594674v2⟩
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