Related papers: Inverse problem for a planar conductivity inclusio…
Polarization tensor corresponding to near zero volume inhomogeneities was introduced in the pioneering work by Capdeboscq-Vogelius \cite{CV1,CV2}. A beautiful application of the polarization tensor to an inverse problem involving…
The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to…
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…
(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…
We study an inverse resonance problem on the line in which we aim at determining a compactly supported and integrable perturbation of a fixed P\"oschl-Teller potential. We define the resonances as the poles of the reflection coefficients…
This paper is concerned with the open problem proposed in Ammari et. al. Commun. Math.Phys, 2013. We first investigate the existence and uniqueness of Generalized Polarization Tensors (GPTs) vanishing structures locally in both two and…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
The purpose of this paper is to propose a non-iterative method for the inverse conductivity problem of recovering multiple small anomalies from the boundary measurements. When small anomalies are buried in a conducting object, the electric…
This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen,…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
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…
The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…
We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…
In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…
We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…
A generalized inversion of block T+H matrix is obtained for the first time. In a particular case when T+H matrix is invertible, the method allows to obtain its inverse matrix without an additional condition of invertibility of the…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…