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This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

偏微分方程分析 · 数学 2025-07-29 Yavar Kian , Hongyu Liu

We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography,…

偏微分方程分析 · 数学 2019-06-18 Christina Knox , Amir Moradifam

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the…

偏微分方程分析 · 数学 2016-07-14 Joonas Ilmavirta , Alden Waters

In this paper, we study the photoacoustic tomography problem for which we seek to recover both the initial state of the pressure field and the wave speed of the medium from the knowledge of a single boundary measurement. The goal is to…

偏微分方程分析 · 数学 2020-07-01 Sebastian Acosta

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…

偏微分方程分析 · 数学 2023-02-08 Yavar Kian , Gunther Uhlmann

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

偏微分方程分析 · 数学 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

We consider an anisotropic hyperbolic equation with memory term: $$ \partial_t^2 u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_ju) + \int^t_0 \sum_{| \alpha| \le 2} b_{\alpha}(x,t,\eta)\partial_x^{\alpha}u(x,\eta) d\eta + F(x,t) $$…

偏微分方程分析 · 数学 2017-12-06 Paola Loreti , Daniela Sforza , Masahiro Yamamoto

This paper concerns thermoacoustic tomography and photoacoustic tomography, two couple-physics imaging modalities that attempt to combine the high resolution of ultrasound and the high contrast capabilities of electromagnetic waves. We give…

偏微分方程分析 · 数学 2015-09-30 Hongyu Liu , Gunther Uhlmann

We consider the inverse problem of determining the initial states or the source term of a hyperbolic equation damped by some non-local time-fractional derivative. This framework is relevant to medical imaging such as thermoacoustic or…

偏微分方程分析 · 数学 2021-11-10 Xinchi Huang , Yavar Kian , Eric Soccorsi , Masahiro Yamamoto

Four problems about recovery of a high-frequency source in the one-dimension heat equation with homogeneous initial-boundary conditions by some information about partial asymptotic of its solution have solved. It is shown, that the source…

偏微分方程分析 · 数学 2017-04-19 Pavel V. Babich , Valeriy B. Levenshtam , Sergey P. Prika

We present a new algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that…

数值分析 · 数学 2015-03-17 Jianliang Qian , Plamen Stefanov , Gunther Uhlmann , Hongkai Zhao

In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…

数值分析 · 数学 2025-08-22 Tianhao Hu , Xinchi Huang , Bangti Jin , Qimeng Quan , Zhi Zhou

In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…

偏微分方程分析 · 数学 2015-03-30 Sebastian Acosta

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…

偏微分方程分析 · 数学 2015-11-05 Maarten V. de Hoop , Lauri Oksanen , Justin Tittelfitz

We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…

偏微分方程分析 · 数学 2018-08-01 Ngoc Do , Leonid Kunyansky

This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…

偏微分方程分析 · 数学 2025-09-22 Xu Wang , Guanlin Yang , Zhidong Zhang

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…

偏微分方程分析 · 数学 2023-04-25 Shiqi Ma , Leyter Potenciano-Machado , Mikko Salo

We investigate the inverse problem of recovering an initial source for the wave equation with fractional attenuation, motivated by photoacoustic tomography (PAT). The attenuation is modeled by a Caputo fractional derivative of order…

偏微分方程分析 · 数学 2025-10-10 Sebastian Acosta , Benjamin Palacios

We study the inverse problem of recovery a non-linearity $f(x,u)$, which is compactly supported in $x$, in the semilinear wave equation $u_{tt}-\Delta u+ f(x,u)=0$. We probe the medium with either complex or real-valued harmonic waves of…

偏微分方程分析 · 数学 2021-07-20 Antônio Sá Barreto , Plamen Stefanov

We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for the nonhomogeneous heat equation in $\Omega\times (0,\infty)$ where $\Omega$ is a bounded domain in $\mathbb{R}^2$ with smooth boundary $\partial\Omega$ from overposed lateral…

偏微分方程分析 · 数学 2019-08-07 William Rundell , Zhidong Zhang
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