English
Related papers

Related papers: An inverse problem for the wave equation with sour…

200 papers

Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in different locations to send and receive waves from each other.…

Machine Learning · Computer Science 2026-01-22 Hanyang Jiang , Yuehaw Khoo , Haizhao Yang

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…

Analysis of PDEs · Mathematics 2021-04-27 Ru-Yu Lai , Hanming Zhou

Dealing with the inverse source problem for the scalar wave equation, we have shown recently that we can reconstruct the space-time dependent source function from the measurement of the wave, collected at a single point $x$ for a large…

Analysis of PDEs · Mathematics 2023-11-15 Soumen Senapati , Mourad Sini , Haibing Wang

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

Analysis of PDEs · Mathematics 2015-09-02 Fikret Gölgeleyen , Masahiro Yamamoto

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

In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…

Analysis of PDEs · Mathematics 2024-05-24 Azizbek Mamanazarov , Durvudkhan Suragan

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

Analysis of PDEs · Mathematics 2023-11-17 Piermarco Cannarsa , Anna Doubova , Masahiro Yamamoto

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…

Analysis of PDEs · Mathematics 2019-09-09 Shahah Almutairi , Ajith Gunaratne

We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…

Analysis of PDEs · Mathematics 2018-01-31 V. G. Romanov , M. Yamamoto

This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation with attenuation. The source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator…

Numerical Analysis · Mathematics 2020-09-30 Peijun Li , Xu Wang

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

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

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither…

Analysis of PDEs · Mathematics 2022-11-02 David Omogbhe , Kamran Sadiq

This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…

Analysis of PDEs · Mathematics 2012-03-07 Guillaume Bal , Eric Bonnetier , Francois Monard , Faouzi Triki

We study the inverse boundary value problem for the linear elastic wave equation in three-dimensional isotropic medium. We show that both the Lam\'e parameters and the density can be uniquely recovered from the boundary measurements under…

Analysis of PDEs · Mathematics 2025-12-22 Jian Zhai

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…

Analysis of PDEs · Mathematics 2026-04-17 Gunther Uhlmann , Yuchao Yi , Jian Zhai

This paper concerns the inverse random source problem of the stochastic Maxwell equations driven by white noise in an inhomogeneous background medium. The well-posedness is established for the direct source problem, and the estimates and…

Analysis of PDEs · Mathematics 2025-03-14 Tianjiao Wang , Xiang Xu , Yue Zhao

We study an inverse problem for the viscoacoustic wave equation, an integro-differential model describing wave propagation in viscoacoustic media with memory in the leading order term. The medium is characterized by a spatially varying…

Analysis of PDEs · Mathematics 2026-03-26 Giovanni Covi , Maarten de Hoop , Mikko Salo

In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…

Analysis of PDEs · Mathematics 2015-12-08 Pengbin Feng , E. T. Karimov

This work deals with an inverse source problem for the biharmonic wave equation. A two-stage numerical method is proposed to identify the unknown source from the multi-frequency phaseless data. In the first stage, we introduce some…

Numerical Analysis · Mathematics 2024-01-08 Yan Chang , Yukun Guo , Yue Zhao
‹ Prev 1 4 5 6 7 8 10 Next ›