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This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…

Analysis of PDEs · Mathematics 2024-02-09 Yi-Hsuan Lin , Teemu Tyni , Philipp Zimmermann

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. We aim at estimating the…

Analysis of PDEs · Mathematics 2019-09-04 Laure Dumaz , Josselin Garnier , Guilhem Lepoultier

We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…

Analysis of PDEs · Mathematics 2021-02-19 Zhengjian Bai , Huaian Diao , Hongyu Liu , Qingle Meng

In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties…

Analysis of PDEs · Mathematics 2025-11-25 Chengyu Wu , Jiaqinq Yang

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak…

Analysis of PDEs · Mathematics 2017-05-04 Juan Carlos Munoz , Michael Ruzhansky , Niyaz Tokmagambetov

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

Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…

Analysis of PDEs · Mathematics 2017-09-07 Peijun Li , Xiaokai Yuan

A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…

Numerical Analysis · Mathematics 2019-11-26 A. B. Bakushinsky , A. S. Leonov

The importance of ultrasound is well established in the imaging of human tissue. In order to enhance image quality by exploiting nonlinear effects, recently techniques such as harmonic imaging and nonlinearity parameter tomography have been…

Analysis of PDEs · Mathematics 2025-02-13 Barbara Kaltenbacher

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

Analysis of PDEs · Mathematics 2020-09-10 Florian Faucher , Otmar Scherzer , Hélène Barucq

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Analysis of PDEs · Mathematics 2017-06-14 Jiaqing Yang , Bo Zhang , Haiwen Zhang

We consider the Bayesian approach to the inverse problem of recovering the shape of an object from measurements of its scattered acoustic field. Working in the time-harmonic setting, we focus on a Helmholtz transmission problem and then…

Analysis of PDEs · Mathematics 2024-10-31 Safiere Kuijpers , Laura Scarabosio

The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…

The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. It is shown that to second order in $k_{0}a$ ($k_{0}$ the wavenumber in the host medium, $a$ the radius of…

Classical Physics · Physics 2009-11-10 Thierry Scotti , Armand Wirgin

An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…

Mathematical Physics · Physics 2007-12-04 Michael V Klibanov , Sergey I Kabanikhin , Dmitriy V Nechaev , Andrey V Kuzhuget

The generation of second and third harmonics by an acoustic wave propagating along one dimension in a weakly nonlinear elastic medium that is loaded harmonically in time with frequency $\omega_0$ at a single point in space, is analyzed by…

Materials Science · Physics 2024-12-11 Fernando Lund

Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…

Optimization and Control · Mathematics 2022-09-28 William W. Symes , Huiyi Chen , Susan E. Minkoff

We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength,…

Numerical Analysis · Mathematics 2022-05-16 Victor Péron

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…

Numerical Analysis · Mathematics 2014-09-16 Manuel Quezada de Luna , David I. Ketcheson