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This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…

Analysis of PDEs · Mathematics 2022-06-22 Barbara Kaltenbacher , William Rundell

This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…

Optimization and Control · Mathematics 2013-10-01 Zui-Cha Deng , Liu Yang

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

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

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

Analysis of PDEs · Mathematics 2024-12-23 S. G. Pyatkov , O. A. Soldatov

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…

Analysis of PDEs · Mathematics 2017-05-12 Kiril Datchev , Maarten V. de Hoop

In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…

Analysis of PDEs · Mathematics 2023-06-28 Matti Lassas , Zhiyuan Li , Zhidong Zhang

We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…

Analysis of PDEs · Mathematics 2021-02-23 Shixu Meng , Othman Oudghiri-Idrissi , Bojan B. Guzina

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…

Analysis of PDEs · Mathematics 2021-12-03 Mourad Sini , Haibing Wang

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…

Analysis of PDEs · Mathematics 2022-08-23 Venkateswaran P. Krishnan , Rakesh , Soumen Senapati

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

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

We consider an inverse source problem for the Helmholtz equation in a bounded domain. The problem is to reconstruct the shape of the support of a source term from the Cauchy data on the boundary of the solution of the governing equation. We…

Analysis of PDEs · Mathematics 2017-05-09 Masaru Ikehata

In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…

Analysis of PDEs · Mathematics 2026-05-13 Bin Wu , Xu Zhu , Wenwen Zhou , Zewen Wang

This paper presents computational analysis of the inverse Stefan type free boundary problem, where information on the boundary heat flux is missing and must be found along with the temperature and the free boundary. We pursue optimal…

Optimization and Control · Mathematics 2018-07-24 Ugur G. Abdulla , Vladislav Bukshtynov , Ali Hagverdiyev

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

Numerical Analysis · Mathematics 2018-06-19 Ramaz Botchorishvili , Tamar Janelidze

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 propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…

Analysis of PDEs · Mathematics 2022-02-25 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…

Analysis of PDEs · Mathematics 2025-11-25 Shiqi Ma