相关论文: Inverse anisotropic conductivity from internal cur…
This paper investigates Calder\'on's problem on a conformally transversally anisotropic manifold $ (M,g) $ of dimension $n \geq 3$, where the conductivity $ a(s,x,p) $ might depend on both the electric potential and the electric field. We…
In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…
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…
Recently, a new strategy to the reconstruction of $f(R)$-gravity models based on the Raychaudhuri equation has been suggested by Choudhury et al. In this paper, utilizing this method, the reconstruction of anisotropic Einstein-Maxwell…
This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large…
We extend monotonicity-based inversion methods to an inverse coefficient problem for the isotropic nonlocal elliptic equation \[ (-\nabla \cdot \sigma \nabla)^s u = 0 \quad \text{in } \Omega \subset \mathbb{R}^n, \] where $0 < s < 1$, $n…
We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…
We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications to transient elastography. Under certain rank-maximality…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term $\epsilon\partial_t u-\nabla\cdot(\gamma\nabla u^m)+\lambda u^q=0$, with…
An accurate functional inequality for Div-BV positive symmetric tensors $A$ in a bounded domain $U\subset\mathbb{R}^n$ arises whenever the tangential part of the normal trace $\gamma_\nu A\sim A\vec\nu$ is a finite measure over $\partial…
We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…
In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic…
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the nonlinear reaction term $f(u)$ in a reaction-diffusion equation from overposed data. These measurements can consist of:…
We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…
We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the…
We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary…
We study inverse conductivity problem for an anisotropic conductivity in $L^\infty$ in bounded and unbounded domains. Also, we give applications of the results in the case when Dirichlet-to-Neumann and Neumann-to-Dirichlet maps are given…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new…