English
Related papers

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

200 papers

This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…

Numerical Analysis · Mathematics 2025-10-13 Yu Sun , Bo Chen , Peng Gao , Qiuyi Li , Yao Sun

Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is…

Analysis of PDEs · Mathematics 2024-01-04 Sergey Grigorievich Pyatkov

This paper is concerned with an inverse transmission problem for recovering the shape of a penetrable rectangular grating sitting on a perfectly conducting plate. We consider a general transmission problem with the coefficient \lambda\neq 1…

Analysis of PDEs · Mathematics 2023-04-24 Jianli Xiang , Guanghui Hu

We prove backward uniqueness for a class of ultraparabolic operators with coupled linear drift. The main difficulty is that the Fourier transform in the degenerate variables turns the coupled drift into a transport operator in the dual…

Analysis of PDEs · Mathematics 2026-05-27 Xiao-Dong Cao , Chao-Jiang Xu , Yan Xu

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…

solv-int · Physics 2009-10-30 M. J. Martins , P. B. Ramos

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…

Analysis of PDEs · Mathematics 2021-04-27 Ru-Yu Lai , Hanming Zhou

We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured…

Mathematical Physics · Physics 2017-09-13 Michael V. Klibanov , Vladimir G. Romanov

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…

Analysis of PDEs · Mathematics 2015-05-28 Mark Hubenthal

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…

Optics · Physics 2021-01-27 Weijin Chen , Qingdong Yang , Yuntian Chen , Wei Liu

A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

Numerical Analysis · Mathematics 2019-04-02 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced…

Optics · Physics 2016-03-09 A. Yamilov , S. Petrenko , R. Sarma , H. Cao

In this short paper, we consider a quadruple $(\Omega, \AA, \theta, \mu)$,where $\AA$ is a $\sigma$-algebra of subsets of $\Omega$, and $\theta$ is a measurable bijection from $\Omega$ into itself that preserves the measure $\mu$. For each…

Probability · Mathematics 2007-05-23 Francois Baccelli , Takis Konstantopoulos

In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic…

Analysis of PDEs · Mathematics 2021-04-20 Genqian Liu

This work addresses the problem of uniquely determining a rotational motion from continuous time-dependent measurements within the frameworks of parallel-beam and diffraction tomography. The motivation stems from the challenge of imaging…

Functional Analysis · Mathematics 2025-10-22 Peter Elbau , Denise Schmutz

This paper is devoted to the uniqueness of inverse acoustic scattering problems with the modulus of near-field data. By utilizing the superpositions of point sources as the incident waves, we rigorously prove that the phaseless near-fields…

Analysis of PDEs · Mathematics 2019-05-22 Deyue Zhang , Fenglin Sun , Yukun Guo , Hongyu Liu

This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special…

Analysis of PDEs · Mathematics 2026-01-19 Kewen Bu , Youjun Deng , Yan Jiang , Kai Zhang

In this paper, we investigate an inverse problem for the radiative transfer equation that is coupled with a heat equation in a nonscattering medium in $\mathbb{R}^n$, $n\geq 2$. The two equations are coupled through a nonlinear blackbody…

Analysis of PDEs · Mathematics 2020-10-12 Christian Klingenberg , Ru-Yu Lai , Qin Li

In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…

Analysis of PDEs · Mathematics 2019-10-14 Francis J. Chung , Jeremy G. Hoskins , John C. Schotland

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

Analysis of PDEs · Mathematics 2021-01-19 Barbara Kaltenbacher , William Rundell