Related papers: Convexification for an Inverse Problem for a 1D Wa…
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…
The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential…
A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…
This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…
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 problem of reconstruction of Cauchy data for the wave equation in $\mathbb{R}^1$ by the measurements of its solution on the boundary of the finite interval. This is a one-dimensional model for the multidimensional problem of…
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 estimate of coefficients of the Convection-Diffusion Equation (CDE) from experimental measurements belongs in the category of inverse problems, which are known to come with issues of ill-conditioning or singularity. Here we concentrate…
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…
An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…
We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…
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…
The recently developed globally convergent numerical method for an inverse medium problem for the Helmholtz equation is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the…
This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave,…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure…
We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…
We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…