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We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial…

Analysis of PDEs · Mathematics 2021-01-21 Li Li

In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…

Numerical Analysis · Mathematics 2017-04-10 Andreas Hauptmann , Matteo Santacesaria , Samuli Siltanen

We study an inverse problem for the fractional Allen-Cahn equation. Our formulation and arguments rely on the asymptotics for the fractional equation and unique continuation properties.

Analysis of PDEs · Mathematics 2025-08-18 Li Li

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the metric tensor in the wave equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the…

Analysis of PDEs · Mathematics 2021-02-11 Mourad Bellassoued

We consider the Calder\`on problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log-log stability in the determination of the isotropic periodic conductivity coefficient from partial…

Analysis of PDEs · Mathematics 2017-11-22 Mourad Choulli , Yavar Kian , Eric Soccorsi

In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…

Analysis of PDEs · Mathematics 2024-04-17 Anamika Purohit

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…

Analysis of PDEs · Mathematics 2018-02-16 Mikko Salo

Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…

Analysis of PDEs · Mathematics 2017-12-07 Masaru Ikehata

We study the inverse problem of unique recovery of a complex-valued scalar function $V:\mathcal M \times \mathbb C\to \mathbb C$, defined over a smooth compact Riemannian manifold $(\mathcal M,g)$ with smooth boundary, given the Dirichlet…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi , Lauri Oksanen

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…

Analysis of PDEs · Mathematics 2020-05-19 Faouzi Triki , Tao Yin

Conductivity equation is studied in piecewise smooth plane domains and with measure-valued current patterns (Neumann boundary values). This allows one to extend the recently introduced concept of bisweep data to piecewise smooth domains,…

Analysis of PDEs · Mathematics 2021-06-14 Otto Seiskari

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\alpha$, with each $D_\alpha$ a homogeneous elastic medium. One typical…

Analysis of PDEs · Mathematics 2017-04-13 Cătălin I. Cârstea , Naofumi Honda , Gen Nakamura

In this paper, we address a particular case of Calder\'on's (or conductivity) inverse problem in dimension two, namely the case of a homogeneous background containing a finite number of cavities (i.e. heterogeneities of infinitely high…

Analysis of PDEs · Mathematics 2018-03-12 Alexandre Munnier , Karim Ramdani

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lam\'e parameters with certain regularity assumptions. In…

Numerical Analysis · Mathematics 2022-12-13 Sarah Eberle , Bastian Harrach , Houcine Meftahi , Taher Rezgui

In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components…

Optimization and Control · Mathematics 2025-06-10 Ching Hong Tam , Frederik Geth , Nadarajah Mithulananthan

In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…

Numerical Analysis · Mathematics 2019-04-08 Bastian Harrach , Houcine Meftahi

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

Numerical Analysis · Mathematics 2018-03-29 Antti Hannukainen , Nuutti Hyvönen , Lauri Mustonen

The paper investigates the sensitivity of the inverse problem of recovering the velocity field in a bounded domain from the boundary dynamic Dirichlet-to-Neumann map (DDtN) for the wave equation. Three main results are obtained: (1)…

Analysis of PDEs · Mathematics 2014-01-07 Gang Bao , Hai Zhang

We consider the Calder\'on problem with partial data in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. We show…

Analysis of PDEs · Mathematics 2016-02-16 Casey Rodriguez

We consider the inverse boundary value problem of the simultaneous determination of the coefficients $\sigma$ and $q$ of the equation $-\mbox{div}(\sigma \nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given…

Analysis of PDEs · Mathematics 2025-05-26 Niall Donlon , Romina Gaburro