Related papers: Inverse source problem for discrete Helmholtz equa…
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different frequencies. An…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
We study an inverse scattering problem at fixed energy for radial magnetic Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) method for solving inverse scattering problems based on an…
We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…
In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…
In this paper we investigate direct and inverse problems for time-fractional pseudo-parabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proved. Also, the stability result of the inverse…
This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…
We consider the Schr\"{o}dinger operator on a finite interval with an $L^1$-potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
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…
We derive conditional stability estimates for inverse scattering problems related to time harmonic magnetic Schr\"odinger equation. We prove logarithmic type estimates for retrieving the magnetic (up to a gradient) and electric potentials…
This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…
We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…