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In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic…

Analysis of PDEs · Mathematics 2024-09-11 Frederic Magoules , Mathieu Menoux , Anna Rozanova-Pierrat

In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The…

Analysis of PDEs · Mathematics 2020-07-23 Frédéric Magoulès , Thi Phuong Kieu Nguyen , Pascal Omnes , Anna Rozanova-Pierrat

In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…

Numerical Analysis · Mathematics 2014-06-23 Giulio Ciraolo , Francesco Gargano , Vincenzo Sciacca

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the…

Numerical Analysis · Mathematics 2023-08-04 Mo Zhou , Jiequn Han , Manas Rachh , Carlos Borges

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…

Analysis of PDEs · Mathematics 2025-06-02 Chun Liu , Guanghui Hu , Tao Yin , Bo Zhang

We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. We prove that the solution has a unique semi-classical measure, which is precisely described in terms of the…

Mathematical Physics · Physics 2013-02-05 Julien Royer

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

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

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

We present Helmholtz or Helmholtz like equations for the approximation of the time-harmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models…

Analysis of PDEs · Mathematics 2019-05-22 Kersten Schmidt , Anastasia Thöns-Zueva

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

Analysis of PDEs · Mathematics 2024-04-23 Faouzi Triki , Kristoffer Linder-Steinlein , Mirza Karamehmedovic

We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…

Analysis of PDEs · Mathematics 2025-09-05 Kuang Huang , Zhiyuan Li , Zhidong Zhang , Zhi Zhou

Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be…

Analysis of PDEs · Mathematics 2025-02-14 Alessandro Felisi

In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by…

Numerical Analysis · Mathematics 2025-11-25 Qianqian Wu , Rongfang Gong , Wei Gong , Ziyi Zhang , Shengfeng Zhu

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…

Analysis of PDEs · Mathematics 2022-07-01 Xuezhu Lu

We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…

Analysis of PDEs · Mathematics 2017-06-28 Nicolas Garcia Trillos , Daniel Sanz-Alonso

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

In this work we investigate the inverse problem of recovering one point source in the heat equation from sparse boundary measurement, i.e., the flux data at several points on the boundary. We prove the unique recovery of the location and…

Analysis of PDEs · Mathematics 2026-03-11 Fangyu Gong , Bangti Jin , Yavar Kian , Sizhe Liu