Related papers: New global stability estimates for monochromatic i…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…
This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This…
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…
Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…
We consider two inverse problems for the multi-channel two-dimensional Schr\"odinger equation at fixed positive energy, i.e. the equation $-\Delta \psi + V(x)\psi = E \psi$ at fixed positive $E$, where $V$ is a matrix-valued potential. The…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies H\"older stability. Importantly, we also show that the point source equation…
In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…
This paper deals with the stability of semi-wavefronts to the following delay non-local monostable equation: $\dot{v}(t,x) = \Delta v(t,x) - v(t,x) + \int_{\R^d}K(y)g(v(t-h,x-y))dy, x \in \R^d,\ t >0;$ where $h>0$ and $d\in\Z_+$. We give…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…