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Related papers: Inverse source problems in elastodynamics

200 papers

This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…

Analysis of PDEs · Mathematics 2020-04-08 Elham Sohrabi

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…

Analysis of PDEs · Mathematics 2025-03-25 Durdiev Durdimurod Kalandarovich

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

In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…

Numerical Analysis · Mathematics 2023-11-23 Zhiyuan Li , Chunlong Sun

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…

Numerical Analysis · Mathematics 2018-05-23 Mirza Karamehmedović , Adrian Kirkeby , Kim Knudsen

Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…

Numerical Analysis · Mathematics 2022-10-17 Bangti Jin , Yavar Kian , Zhi Zhou

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…

Numerical Analysis · Mathematics 2017-08-03 Guan Wang , Fuming Ma , Yukun Guo , Jingzhi Li

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…

Numerical Analysis · Mathematics 2021-01-14 Xiaoli Feng , Meixia Zhao , Peijun Li , Xu Wang

In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

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 paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…

Analysis of PDEs · Mathematics 2023-03-22 Lei Zhang , Yue Zhao

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…

Analysis of PDEs · Mathematics 2020-03-13 Guanghui Hu , Jingzhi Li

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Numerical Analysis · Mathematics 2026-05-08 Siyu Cen , Bangti Jin , Yavar Kian , Zhi Zhou

We are concerned with increasing stability in the inverse source problems for the time-dependent Maxwell equations in R^3 , where the source term is compactly supported in both time and spatial variables. By using the Fourier transform,…

Analysis of PDEs · Mathematics 2024-02-27 Suliang Si

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

Analysis of PDEs · Mathematics 2007-05-23 Kenrick Bingham , Yaroslav Kurylev , Matti Lassas , Samuli Siltanen

The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the…

Analysis of PDEs · Mathematics 2019-09-04 Johannes Elschner , Guanghui Hu