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We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many…

Analysis of PDEs · Mathematics 2020-02-12 Tuhin Ghosh , Angkana Rüland , Mikko Salo , Gunther Uhlmann

In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…

Analysis of PDEs · Mathematics 2016-01-22 M. S. Salakhitdinov , E. T. Karimov

We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calder\'on problem by using an integral identity. We also determine…

Analysis of PDEs · Mathematics 2021-06-07 Li Li

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in…

Analysis of PDEs · Mathematics 2013-03-01 Valter Pohjola

We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…

Analysis of PDEs · Mathematics 2024-07-22 Marcus Corbett , Fernando Guevara Vasquez , Alexander Royzman , Guang Yang

We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain…

Analysis of PDEs · Mathematics 2019-04-01 Matti Lassas , Tony Liimatainen , Yi-Hsuan Lin , Mikko Salo

The inverse problems about fractional Calder\'on problem and fractional Schr\"odinger equations are of interest in the study of mathematics. In this paper, we propose the inverse problem to simultaneously reconstruct potentials and sources…

Numerical Analysis · Mathematics 2024-09-26 Xinyan Li

We discuss the use of differential sampling method to image local perturbations in anisotropic periodic layers, extending earlier works on the isotropic case. We study in particular the new interior transmission problem that is associated…

Numerical Analysis · Mathematics 2018-11-09 Thi-Phong Nguyen

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

Analysis of PDEs · Mathematics 2025-05-21 Yuchao Yi , Yang Zhang

We prove exponential instability properties for the fractional Calder\'on problem and the conductivity formulation of the fractional Calder\'on problem in the regime of fractional powers $s\in (0,1)$. We particularly focus on two settings:…

Analysis of PDEs · Mathematics 2024-05-15 Hendrik Baers , Giovanni Covi , Angkana Rüland

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We…

Analysis of PDEs · Mathematics 2015-05-13 D. Dos Santos Ferreira , C. E. Kenig , M. Salo , G. Uhlmann

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Analysis of PDEs · Mathematics 2024-05-03 Rohit Kumar Mishra , Anamika Purohit , Manmohan Vashisth

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n, n\geq2$, can uniquely determine, in a nonlinear magnetic Schr\"odinger equation, the vector-valued…

Analysis of PDEs · Mathematics 2020-07-07 Ru-Yu Lai , Ting Zhou

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…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear…

Analysis of PDEs · Mathematics 2011-06-22 Mikko Salo , Xiao Zhong

Let $\hat \Omega \subset \mathbb R^2$ be a bounded domain with smooth boundary and $\hat \sigma$ a smooth anisotropic conductivity on $\hat \Omega$. Starting from the Dirichlet-to-Neumann operator $\Lambda_{\hat \sigma}$ on $\partial \hat…

Analysis of PDEs · Mathematics 2014-02-07 Gennadi Henkin , Matteo Santacesaria

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

Analysis of PDEs · Mathematics 2024-06-04 Xiaoxu Xu , Guanghui Hu

This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shr\"odinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and…

Analysis of PDEs · Mathematics 2020-02-24 Gang Bao , Yuantong Liu , Faouzi Triki