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This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method…
Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of…
Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that…
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…
This work considers a time domain inverse acoustic obstacle scattering problem due to passive data. Motivated by the Helmholtz-Kirchhoff identity in the frequency domain, we propose to relate the time domain measurement data in passive…
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions,…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
A mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory…
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…
We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…
We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify the locations and shapes of moving inhomogeneities when very…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…
In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain,…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
We consider an inverse boundary value problem for the equation $\nabla\cdot(\sigma-i\omega\epsilon)\nabla u=0$ in a given bounded domain $\Omega$ at a fixed $\omega>0$. $\sigma$ and $\epsilon$ denote the conductivity and permittivity of the…