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Related papers: Uniqueness and Non-uniqueness in inverse radiative…

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This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Analysis of PDEs · Mathematics 2025-04-23 Joseph Kraisler , Wei Li , Kui Ren , John C. Schotland , Yimin Zhong

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither…

Analysis of PDEs · Mathematics 2022-11-02 David Omogbhe , Kamran Sadiq

We revisit the instability properties of the recovery of the absorption coefficient for the radiative transfer equation in the diffusive regime. To this end, we develop a rather robust framework building on [Koch-R\"uland-Salo, 2021] which…

Analysis of PDEs · Mathematics 2026-05-21 Elena Demattè , Alessandro Felisi , Angkana Rüland , Juan J. L. Velázquez

The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a…

Mathematical Physics · Physics 2007-05-23 Tuncay Aktosun

It is shown that the operator algebraic setting of local quantum physics leads to a uniqueness proof for the inverse scattering problem. The important mathematical tool is the thermal KMS aspect of wedge-localized operator algebras and its…

High Energy Physics - Theory · Physics 2011-07-19 Bert Schroer

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed…

Mathematical Physics · Physics 2015-05-20 A. G. Ramm

In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…

Analysis of PDEs · Mathematics 2023-05-09 Barbara Kaltenbacher

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…

Analysis of PDEs · Mathematics 2015-09-02 Matias Courdurier , Francois Monard , Axel Osses , Francisco Romero

We consider the inverse problem of the recovery of the gauge field in R^2 modulo gauge transformations from the non-abelian Radon transform.A global uniqueness theorem is proven for the case when the gauge field has a compact support.

Analysis of PDEs · Mathematics 2015-07-06 Gregory Eskin

This paper is concerned with the unique identification of the shape of a scatterer through a single far-field pattern in an inverse elastic medium scattering problem with a generalized transmission boundary condition. The uniqueness issue…

Analysis of PDEs · Mathematics 2023-12-06 Huaian Diao , Ruixiang Tang , Hongyu Liu , Jiexin Tang

In a finite-dimensional Euclidian space we consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering…

Spectral Theory · Mathematics 2013-11-13 Mikhail Ignatyev

We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…

Analysis of PDEs · Mathematics 2026-04-21 Kui Ren , Yimin Zhong

We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…

Analysis of PDEs · Mathematics 2019-08-20 Guillaume Bal , François Monard

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Marlena Nowaczyk , Bruce Alastair Watson

We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a…

Analysis of PDEs · Mathematics 2013-08-28 Guanghui Hu , Hongyu Liu

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…

Analysis of PDEs · Mathematics 2008-03-31 Plamen Stefanov , Gunther Uhlmann

We consider the inverse problem for the general transport equation with external field, source term and absorption coefficient. We show that the source and the absorption coefficients can be uniquely reconstructed from the boundary…

Analysis of PDEs · Mathematics 2019-04-24 Ru-Yu Lai , Qin Li

In this paper, we consider the inverse spectral problem of determining the spherically symmetric refractive index in a bounded spherical region of radius $b$. Instead of the usual case of the refractive index $\rho\in W^2_2$, by using…

Spectral Theory · Mathematics 2025-09-29 Tao Liu , Kang Lyu , Guangsheng Wei , Chuan-Fu Yang