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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 prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary,…

Analysis of PDEs · Mathematics 2011-05-24 Pierre Albin , Colin Guillarmou , Leo Tzou , Gunther Uhlmann

This paper is concerned with inverse source problems for the time-dependent Lam\'e system in an unbounded domain corresponding to the exterior of a bounded cavity or the full space $\R^3$. If the time and spatial variables of the source…

Analysis of PDEs · Mathematics 2019-07-04 Guanghui Hu , Yavar Kian

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 study inverse boundary problems for magnetic Schr\"odinger operators on a compact Riemannian manifold with boundary of dimension $\ge 3$. In the first part of the paper we are concerned with the case of admissible geometries, i.e.…

Analysis of PDEs · Mathematics 2018-08-01 Katya Krupchyk , Gunther Uhlmann

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Analysis of PDEs · Mathematics 2025-11-27 Xiaoxu Xu , Guanghui Hu

We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem…

Differential Geometry · Mathematics 2022-02-24 Nadine Große , Simone Murro

In this paper a compact Riemannian manifold with strictly convex boundary is reconstructed from its partial travel time data. This data assumes that an open measurement region on the boundary is given, and that for every point in the…

Differential Geometry · Mathematics 2022-04-20 Ella Pavlechko , Teemu Saksala

We study inverse boundary problems for the magnetic Schr\"odinger operator with H\"older continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n greater…

Analysis of PDEs · Mathematics 2023-11-09 Salem Selim , Lili Yan

We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…

Analysis of PDEs · Mathematics 2017-07-18 Gregory Eskin

We show that a complete Riemannian manifold, as well as time independent smooth lower order terms appearing in a first order symmetric perturbation of a Riemannian wave operator can be uniquely recovered, up to the natural obstructions,…

Analysis of PDEs · Mathematics 2025-05-01 Teemu Saksala , Andrew Shedlock

We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…

Analysis of PDEs · Mathematics 2022-10-11 Shitao Liu , Antonio Pierrottet , Scott Scruggs

In this conference published in 1997 some problems on the geodesics of a Lorentzian manifold concerning causality and infinite-dimensional variational methods, are pointed out. Even though a big progress on many of these questions have been…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Miguel Sanchez

This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…

Analysis of PDEs · Mathematics 2018-10-30 Mourad Bellassoued , Mourad Choulli , Dos Santos Ferreira , Yavar Kian , Plamen Stefanov

In this paper, we consider a Cauchy problem for a first-order hyperbolic equation with time-dependent coefficients. Cauchy data are given on a lateral subboundary and we obtain local H\"older stabilities for inverse source and coefficient…

Analysis of PDEs · Mathematics 2025-10-13 Giuseppe Floridia , Hiroshi Takase

The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a…

Analysis of PDEs · Mathematics 2020-01-14 Nikolai Dokuchaev

Consider a real-analytic orientable connected complete Riemannian manifold $M$ with boundary of dimension $n\ge 2$ and let $k$ be an integer $1\le k\le n$. In the case when $M$ is compact of dimension $n\ge 3$, we show that the manifold and…

Analysis of PDEs · Mathematics 2010-07-07 Katsiaryna Krupchyk , Matti Lassas , Gunther Uhlmann

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a H\"older stability in the determining of the…

Analysis of PDEs · Mathematics 2016-07-07 L. Beilina , M. Cristofol , S. Li

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in $\R^n$ with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the…

Analysis of PDEs · Mathematics 2015-07-08 Gregory Eskin

A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…

Analysis of PDEs · Mathematics 2015-05-14 Malcolm Brown , Marco Marletta , Juan Manuel Reyes