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We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

Analysis of PDEs · Mathematics 2023-11-17 Piermarco Cannarsa , Anna Doubova , Masahiro Yamamoto

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three…

Analysis of PDEs · Mathematics 2022-09-12 Youzi He , Hongjie Li , Hongyu Liu , Xianchao Wang

We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…

Analysis of PDEs · Mathematics 2023-09-01 Shiqi Ma , Suman Kumar Sahoo , Mikko Salo

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…

Optics · Physics 2015-05-14 Guillaume Bal , John C Schotland

This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…

Numerical Analysis · Mathematics 2020-08-26 Barbara Kaltenbacher , William Rundell

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…

Numerical Analysis · Mathematics 2020-07-20 Rashmi Murthy , Yi-Hsuan Lin , Kwancheol Shin , Jennifer L. Mueller

A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…

Analysis of PDEs · Mathematics 2015-06-25 Sarah Jane Hamilton , Matti Lassas , Samuli Siltanen

This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…

Numerical Analysis · Mathematics 2023-09-25 Tran H. Lan , Dinh-Liem Nguyen

We consider the issues of stability and reconstruction of the electrical anisotropic conductivity of biological tissues in a domain $\Omega\subset\mathbb{R}^3$ by means of the hybrid inverse problem of magneto-acoustic tomography with…

Analysis of PDEs · Mathematics 2022-08-01 Niall Donlon , Romina Gaburro , Shari Moskow , Isaac Woods

We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…

Analysis of PDEs · Mathematics 2026-03-10 Cătălin I. Cârstea , Tuhin Ghosh

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…

Optimization and Control · Mathematics 2018-08-29 B. J. Adesokan , Kim Knudsen , Venkateswaran P. Krishnan , Souvik Roy

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable…

Numerical Analysis · Mathematics 2012-10-03 Stéphane Brull , Fabrice Deluzet , Alexandre Mouton

This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…

Complex Variables · Mathematics 2017-05-09 Vincent Michel

The problem of reconstructing the drift of a diffusion in $\erre^d$, $d\geq 2$, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of…

Probability · Mathematics 2007-06-13 Sergio Albeverio , Carlo Marinelli

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated…

Analysis of PDEs · Mathematics 2015-06-17 Guillaume Bal , Cédric Bellis , Sébastien Imperiale , François Monard

We consider the two dimensional quantitative imaging problem of recovering a radiative source inside an absorbing and scattering medium from knowledge of the outgoing radiation measured at the boundary. The medium has an anisotropic…

Numerical Analysis · Mathematics 2021-01-21 Hiroshi Fujiwara , Kamran Sadiq , Alexandru Tamasan

We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…

Analysis of PDEs · Mathematics 2026-05-13 Piermarco Cannarsa , Veronica Danesi , Anna Doubova

We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…

Analysis of PDEs · Mathematics 2019-08-20 Guillaume Bal , François Monard

A radial transverse resonance model for two cylindrical concentric layers with different complex dielectric constants is presented. An inverse problem with four unknowns - 3 physical material parameters and one dimensional dielectric layer…

Optics · Physics 2016-03-24 Anders Eriksson , Truls Martin Larsen , Larisa Beilina