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This paper is concerned with the inverse acoustic scattering problems of reconstructing time-dependent multiple point sources and sources on a curve $L$ of the form $\lambda(t)\tau(x)\delta_L(x)$. A direct sampling method with a novel…

Numerical Analysis · Mathematics 2023-09-07 Jiaru Wang , Bo Chen , Qingqing Yu , Yao Sun

We deal with the problem of determining the shape of an inclusion embedded in a homogenous background medium. The multifre-quency electrical impedance tomography is used to image the inclusion. For different frequencies, a current is…

Analysis of PDEs · Mathematics 2019-03-21 Jin Cheng , Mourad Choulli , Shuai Lu

In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…

Analysis of PDEs · Mathematics 2025-08-19 Dian Feng , Yikan Liu , Shuai Lu

The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…

Numerical Analysis · Mathematics 2016-10-26 Aleksandr E. Kolesov , Michael V. Klibanov , Loc H. Nguyen , Dinh-Liem Nguyen , Nguyen T. Thanh

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…

Optimization and Control · Mathematics 2022-09-28 William W. Symes

This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…

Numerical Analysis · Mathematics 2025-06-03 Xiaoli Liu , Shixu Meng , Jialu Tian , Bo Zhang

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Analysis of PDEs · Mathematics 2025-11-27 Xiaoxu Xu , Guanghui Hu

A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…

Numerical Analysis · Mathematics 2012-11-28 Michael O'Neil , Leslie Greengard , Andras Pataki

For many wave propagation problems with random sources it has been demonstrated that cross correlations of wave fields are proportional to the imaginary part of the Green function of the underlying wave equation. This leads to the inverse…

Analysis of PDEs · Mathematics 2018-04-11 Alexey Agaltsov , Thorsten Hohage , Roman Novikov

In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…

Analysis of PDEs · Mathematics 2025-03-07 Pu-Zhao Kow , Mikko Salo , Sen Zou

In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in $\mathbb R^3$. Firstly, to connect the boundary data with the unknown source, we…

Analysis of PDEs · Mathematics 2021-02-10 Peijun Li , Xiaohua Yao , Yue Zhao

In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our…

Analysis of PDEs · Mathematics 2025-06-04 Jianli Xiang

This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact…

Analysis of PDEs · Mathematics 2015-06-22 David P. Hewett , Aaron Morris

This paper is concerned with the numerical simulation of three dimensional time-dependent inverse source problems of acoustic waves. The reconstructions of both multiple stationary point sources and a moving point source are considered. The…

Numerical Analysis · Mathematics 2020-08-26 Bo Chen , Yukun Guo , Fuming Ma , Yao Sun

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh

Several strategies are available for solving the inverse source problem in electromagnetics. Among them, many have been focusing in retrieving Love currents by solving, after regularization, for Love's electric and magnetic currents. In…

Numerical Analysis · Mathematics 2023-05-19 Paolo Ricci , Adrien Merlini , Francesco P. Andriulli

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…

Analysis of PDEs · Mathematics 2023-01-02 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…

Numerical Analysis · Mathematics 2022-08-03 T. Chaumont-Frelet , P. Vega

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian
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