Related papers: One dimensional inverse problem in photoacoustic. …
We consider the problem of reconstruction of the Cauchy data for the wave equation in $\mathbb{R}^3$ and $\mathbb{R}^2$ by the measurements of its solution on the boundary of the unit ball.
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic…
The inverse problem of finding the refraction coefficient of a shallow ocean from the observation of the extra Cauchy data for the acoustic field at the surface of the ocean is studied. Uniqueness theorem is proved and a reconstruction…
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and…
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…
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…
Consider a real-analytic orientable connected complete Riemannian manifold $M$ with boundary of dimension $n\ge 2$ and let $k$ be an integer $1\le k\le n$. In the case when $M$ is compact of dimension $n\ge 3$, we show that the manifold and…
We consider the classical Cauchy problem for a system of equations describing 3D arbitrary electrostatic oscillations of the cold plasma and introduce an iteration procedure that allows estimating the blow-up time from below. This procedure…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…
We consider image reconstruction in full-field photoacoustic tomography, where 2D projections of the full 3D acoustic pressure distribution at a given time T>0 are collected. We discuss existing results on the stability and uniqueness of…
We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…
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…