Inverse scattering problem for a two dimensional random potential
type: Item
instance of: scholarly article
title: Inverse scattering problem for a two dimensional random potential
zbMATH Open document ID: 1203.35292
author: M. Lassas
author: Lassi Päivärinta
author: Eero Saksman
published in: Communications in Mathematical Physics
publication date: 2008-05-27T00:00:00Z
review text: The setup of the stochastic scattering problem consists in the two-dimensional Schrödinger equation with outgoing radiation condition, where the potential is assumed to be a random generalized function supported in a bounded and simply connected domain in the plane. It is assumed also that its covariance operator is a classical pseudodifferential operator. It is proved that the backscattered field, obtained from a single realization of the potential \(q\), determines uniquely the principal symbol of the covariance operator of \(q\). The main tools used to this end are a combination of harmonic and microlocal analysis with stochastic methods.
reviewed by: Elisa Alòs
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 81U40
zbMATH DE Number: 5279030
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: inverse problem
zbMATH Keywords: stochastic scattering
Wikidata QID: Q109553827
MaRDI profile type: Publication
full work available at URL: s00220-008-0416-6
OpenAlex ID: W2067107552
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DOI: 10.1007/S00220-008-0416-6
description: scientific article; zbMATH DE number 5279030