Related papers: Inverse source problem for discrete Helmholtz equa…
We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured…
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…
In this paper, we study the meromorphic continuation of the resolvent for the Schr\"{o}dinger operator in a three-dimensional planar waveguide. We prove the existence of a resonance-free region and an upper bound for the resolvent. As an…
This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
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…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical…
The main purpose of this paper is to develop further the integrated theory of the probe and singular sources methods (IPS) which may work for a group of inverse obstacle problems. Here as a representative and typical member of the group, an…
We solve inverse scattering problem for Schr\"odinger operators with compactly supported potentials on the half line. We discretize S-matrix: we take the value of the S-matrix on some infinite sequence of positive real numbers. Using this…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…