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We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

Numerical Analysis · Mathematics 2022-11-23 Guang Lin , Zecheng Zhang , Zhidong Zhang

In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff…

Analysis of PDEs · Mathematics 2010-10-14 Shitao Liu

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

In this work, we propose a full-waveform technique for the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion. The approach is formulated in the frequency domain, and…

Computational Physics · Physics 2020-07-15 Alan A. S. Amad , Antonio A. Novotny , Bojan B. Guzina

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Numerical Analysis · Mathematics 2025-07-11 Yunqing Huang , Shihan Zhang

In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…

Analysis of PDEs · Mathematics 2025-08-11 Rahmonov Askar Ahmadovich

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Analysis of PDEs · Mathematics 2017-06-14 Jiaqing Yang , Bo Zhang , Haiwen Zhang

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…

Analysis of PDEs · Mathematics 2016-01-22 M. S. Salakhitdinov , E. T. Karimov

The inverse problem of finding the velocity profile from the surface measurements of acoustic field is considered. The dimensionalities of the data and of the unknown velocity profile are equal, both are equal 3. Analytical explicit…

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

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

Analysis of PDEs · Mathematics 2020-09-10 Florian Faucher , Otmar Scherzer , Hélène Barucq

This paper is concerned with the uniqueness on two inverse moving source problems in electrodynamics with partial boundary data. We show that (1) if the temporal source function is compactly supported, then the spatial source profile…

Analysis of PDEs · Mathematics 2019-07-24 Guanghui Hu , Yavar Kian , Peijun Li , Yue Zhao

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 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

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…

Analysis of PDEs · Mathematics 2019-11-04 Chan Liu , Jin Wen , Zhidong Zhang

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…

Analysis of PDEs · Mathematics 2016-07-25 Peijun Li , Ganghua Yuan

This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…

Analysis of PDEs · Mathematics 2023-07-14 Peijun Li , Ying Liang

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been…

Numerical Analysis · Mathematics 2023-10-18 Guang Lin , Na Ou , Zecheng Zhang , Zhidong Zhang

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 is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…

Numerical Analysis · Mathematics 2017-02-09 Frederic Weidling , Thorsten Hohage