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We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…

Analysis of PDEs · Mathematics 2015-11-05 Maarten V. de Hoop , Lauri Oksanen , Justin Tittelfitz

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

The inverse source problem for the Helmholtz equation poses significant challenges, particularly when sources exhibit complex or discontinuous geometries. Traditional numerical methods suffer from prohibitive computational costs, while…

Mathematical Physics · Physics 2025-10-13 Xinwei Hu , Jingrun Chen , Haijun Yu

In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All…

Analysis of PDEs · Mathematics 2021-12-22 Rainer Mandel , Zoïs Moitier , Barbara Verfürth

Quantum electro-mechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties which ultimately stem from the Heisenberg Uncertainty Principle. A simple example of this is expected to…

Quantum Physics · Physics 2014-10-15 A. J. Weinstein , C. U. Lei , E. E. Wollman , J. Suh , A. Metelmann , A. A. Clerk , K. C. Schwab

This work is dedicated to uniqueness and numerical algorithms for determining the point sources of the biharmonic wave equation using scattered fields at sparse sensors. We first show that the point sources in both $\mathbb{R}^2$ and…

Analysis of PDEs · Mathematics 2025-03-11 Xiaodong Liu , Qingxiang Shi , Jing Wang

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…

Analysis of PDEs · Mathematics 2020-07-13 Boya Liu

In this study, we focus on identifying solution and an unknown space-dependent coefficient in a space-time fractional differential equation by employing fractional Taylor series method. The substantial advantage of this method is that we…

Analysis of PDEs · Mathematics 2021-06-08 Mine Aylin Bayrak , Ali Demir

This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…

Numerical Analysis · Mathematics 2024-12-10 Yan Chang , Yukun Guo , Zhipeng Yang , Yue Zhao

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 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

The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…

Analysis of PDEs · Mathematics 2009-02-02 M. Agranovsky , P. Kuchment , L. Kunyansky

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multicomponent gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an…

Fluid Dynamics · Physics 2017-09-18 Luca Magri

The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set…

Numerical Analysis · Mathematics 2019-07-23 Zhiliang Deng , Xiaomei Yang , Jiangfeng Huang

We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…

Classical Analysis and ODEs · Mathematics 2016-04-26 Khaled M. Furati , Olaniyi S. Iyiola , Kassem Mustapha

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

Numerical Analysis · Mathematics 2020-04-10 Zhaoxing Li , Yanfang Liu , Jiguang Sun , Liwei Xu

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

Assigning boundary conditions, such as acoustic impedance, to the frequency domain thermoviscous wave equations (TWE), derived from the linearized Navier-Stokes equations (LNSE) poses a Helmholtz problem, solution to which yields a discrete…

Computational Physics · Physics 2017-08-03 Danish Patel , Prateek Gupta , Carlo Scalo

In thermoacoustic and photoacoustic tomography an electromagnetic wave is sent through a medium, heating it and therefore generating an elastic expansion that in turns generates an acoustic wave that is measured outside the medium. The…

Analysis of PDEs · Mathematics 2023-02-08 Yavar Kian , Gunther Uhlmann