Related papers: Inverse Elastic Scattering for a Random Source
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
Through coupled physics, we study an early-warning inverse source problem for the elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and…
The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
This work is dedicated to a novel sampling method for accurately reconstructing elastic and electromagnetic sources from the far field patterns. We show that the proposed indicators in the form of integrals with full far field patterns are…
This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…
We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
We present two applications of the integro-differential volume equation for the eigenstrain, building on Eshelby's inclusion method [15,16], in the contexts of both static and dynamic linear elasticity. The primary objective is to address…
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…
Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…
We consider one-dimensional inverse scattering in attenuating media where both the reflectivity and loss distributions are unknown. Mathematically, this corresponds to recovering the coefficients of a damped wave operator, or equivalently,…
In this paper, we study an inverse scattering problem at fixed energy on three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the topology of toric cylinders and satisfying the Robertson condition. On these manifolds the…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
The inverse-scattering problem of an inhomogeneous material has been of interest for many years, and was generally addressed with various optimization techniques. In this paper, we suggest an optimization-free method for solving the…