Related papers: An approximate method for solving inverse scatteri…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
The focus of this paper is the study of the inverse point-source scattering problem, specifically in relation to a certain class of electric potentials. Our research provides a novel uniqueness result for the inverse problem with local…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
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…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously…
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density…
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…