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It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…

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

Uniqueness is proven for two 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex…

Mathematical Physics · Physics 2013-04-01 Michael V. Klibanov

We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…

Analysis of PDEs · Mathematics 2019-04-09 J Liu , X. Liu , J. Sun

We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by…

Analysis of PDEs · Mathematics 2021-11-03 Cristóbal J. Meroño , Leyter Potenciano-Machado , Mikko Salo

In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

Analysis of PDEs · Mathematics 2021-04-27 Ibtissem Ben Aïcha , Guanghui Hu , Manmohan Vashisth , Jun Zou

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong 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 deal with the problem of reconstructing material coefficients from the farfields they generate. By embedding small (single) inclusions to these media, located at points $z$ in the support of these materials, and measuring the farfields…

Analysis of PDEs · Mathematics 2016-10-20 Ahmed Alsaedi , Faris Alzahrani , Durga Prasad Challa , Mokhtar Kirane , Mourad Sini

The problem to be studied in this work is within the context of coefficient identification problems for the wave equation. More precisely, we consider the problem of reconstruction of the refractive index (or equivalently, the dielectric…

Mathematical Physics · Physics 2013-06-14 Nguyen Trung Thành , Larisa Beilina , Michael V. Klibanov , Michael A. Fiddy

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

Analysis of PDEs · Mathematics 2024-10-23 Xiaohua Jing , Zhiyuan Li , Masahiro Yamamoto

The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…

Mathematical Physics · Physics 2016-09-07 A. G. Ramm

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

Analysis of PDEs · Mathematics 2020-04-15 Isaac Harris , Andreas Kleefeld

The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…

Numerical Analysis · Mathematics 2026-04-29 Yukun Guo , Xiaodong Liu

We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…

Numerical Analysis · Mathematics 2017-06-07 Dinh-Liem Nguyen , Michael V. Klibanov , Loc H. Nguyen , Aleksandr E. Kolesov , Michael A. Fiddy , Hui Liu

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

Numerical Analysis · Mathematics 2025-04-22 Lingyun Qiu , Jiwoon Sim

Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…

Analysis of PDEs · Mathematics 2013-05-07 Jiaqing Yang , Bo Zhang

In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same position as the support of the initial data. The…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…

Analysis of PDEs · Mathematics 2016-09-14 Jaan Janno , Kairi Kasemets

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

In this paper, we give a positive answer to a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far…

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