Alexey Agaltsov

Riemann--Hilbert problem approach for two-dimensional flow inverse scattering

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Finding scattering data for a time-harmonic wave equation with first order perturbation from the Dirichlet-to-Neumann map

Abstract We present formulas and equations for finding scattering data from the Dirichlet-to-Neumann map for a time-harmonic wave equation with first order perturbation with compactly supported coefficients. We assume that the coefficients are matrix-valued in general. To our knowledge, these results are new even for the general scalar case.

Uniqueness and non-uniqueness in acoustic tomography of moving fluid

Abstract We consider a model time-harmonic wave equation of acoustic tomography of moving fluid in an open bounded domain in ℝd, d ≥ 2, with variable sound speed c, density ρ, fluid velocity v and absorption coefficient α. We give global uniqueness results for related inverse boundary value problem for the cases of boundary measurements given for two and for three fixed frequencies. Besides, we also give a non-uniqueness result for this inverse problem for the case of boundary measurements given for all frequencies.

On the injectivity of the generalized Radon transform arising in a model of mathematical economics

In the present article we consider the uniqueness problem for the generalized Radon transform arising in a mathematical model of production. We prove uniqueness theorems for this transform and for the profit function in the corresponding model of production. Our approach is based on the multidimensional Wieners approximation theorems.

Error Estimates for Phaseless Inverse Scattering in the Born Approximation at High Energies

We study explicit formulas for phaseless inverse scattering in the Born approximation at high energies for the Schrödinger equation with compactly supported potential in dimension

A characterization theorem for a generalized radon transform arising in a model of mathematical economics

d \ge 2

An iterative approach to monochromatic phaseless inverse scattering

d ≥ 2 . We obtain error estimates for these formulas in the configuration space.