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In this paper, we provide an analytical study of the transmission eigenvalue problem in the context of biharmonic scattering with a penetrable obstacle. We will assume that the underlying physical model is given by an infinite elastic…

Analysis of PDEs · Mathematics 2025-10-10 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…

Numerical Analysis · Mathematics 2017-04-05 Roland Griesmaier , Christian Schmiedecke

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered $P$-parts or $S$-parts of the far field pattern, corresponding to all the incident plane waves of pressure or…

Analysis of PDEs · Mathematics 2013-11-19 Manas Kar , Mourad Sini

We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…

Analysis of PDEs · Mathematics 2022-02-14 Roland Griesmaier , Marvin Knöller , Rainer Mandel

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

The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (probes). For a penetrable object with known sound speed, this…

Numerical Analysis · Mathematics 2023-02-15 Carlos Borges , Manas Rachh , Leslie Greengard

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 paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…

Analysis of PDEs · Mathematics 2024-04-11 Chun Liu , Guanghui Hu , Jianli Xiang , Jiayi Zhang

The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…

Analysis of PDEs · Mathematics 2023-06-09 Masaru Ikehata

We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…

Analysis of PDEs · Mathematics 2022-09-20 Théophile Chaumont-Frelet , Euan A. Spence

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

In this paper, we consider the obstacle scattering problem for biharmonic equations with a Dirichlet boundary condition in both two and three dimensions. Some basic properties are first derived for the biharmonic scattering solutions, which…

Analysis of PDEs · Mathematics 2025-10-16 Chengyu Wu , Jiaqing Yang

In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned…

Analysis of PDEs · Mathematics 2022-04-07 Huaian Diao , Xiaoxu Fei , Hongyu Liu , Ke Yang

We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…

Analysis of PDEs · Mathematics 2020-05-05 Emilia Blåsten , Hongyu Liu

For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…

Numerical Analysis · Mathematics 2018-05-24 Andrew Gibbs , Stephen Langdon , Andrea Moiola

In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…

Numerical Analysis · Mathematics 2024-02-23 Drossos Gintides , Leonidas Mindrinos

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

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu