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Let $\Omega\subset \Bbb R^2$ be a bounded domain with $\partial\Omega\in C^\infty$ and $L$ be a positive number. For a three dimensional cylindrical domain $Q=\Omega\times (0,L)$, we obtain some uniqueness result of determining a…

Mathematical Physics · Physics 2015-06-12 Oleg Yu Imanuvilov , Masahiro Yamamoto

In this paper we investigate the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary. Namely,…

Analysis of PDEs · Mathematics 2015-07-27 Mourad Bellassoued , Yavar Kian , Eric Soccorsi

In this article, we investigate an inverse problem for a semi-linear wave equation posed on bounded domain in $\mathbb{R}^{n+1}$, with $n \geq 2$. Our primary objective is to reconstruct the damping coefficient, the linear and nonlinear…

Analysis of PDEs · Mathematics 2026-04-07 Rahul Bhardwaj , Mandeep Kumar , Manmohan Vashisth

We show in two dimensions that measuring Dirichlet data for the conductivity equation on an open subset of the boundary and, roughly speaking, Neumann data in slightly larger set than the complement uniquely determines the conductivity on a…

Analysis of PDEs · Mathematics 2008-09-19 Oleg Yu. Imanuvilov , Gunther Uhlmann , masahiro Yamamoto

We consider an inverse spectral problem on a quantum graph associated with the square lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the Dirichlet-to-Neumann map for a boundary value…

Mathematical Physics · Physics 2023-06-26 Dongjie Wu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

We consider the multidimensional Borg-Levinson theorem of determining both the magnetic field $dA$ and the electric potential $V$, appearing in the Dirichlet realization of the magnetic Schr\"odinger operator $H=(-{\rm i}\nabla+A)^2+V$ on a…

Analysis of PDEs · Mathematics 2016-10-14 Yavar Kian

We consider the dynamical system with boundary control for the vector Schr\"odinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the…

Analysis of PDEs · Mathematics 2025-05-12 Sergei Avdonin , Alexander Mikhaylov , Victor Mikhaylov , Jeff Park

We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…

Analysis of PDEs · Mathematics 2026-03-30 Sergei Avdonin , Matti Lassas , Jinpeng Lu , Medet Nursultanov , Lauri Oksanen

This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in…

Analysis of PDEs · Mathematics 2020-02-20 Mourad Bellassoued , Ibtissem Ben Aïcha , Zouhour Rezig

We study the inverse problem of determining a magnetic Schr\"odinger operator in an unbounded closed waveguide from boundary measurements. We consider this problem with a general closed waveguide in the sense that we only require our…

Analysis of PDEs · Mathematics 2019-01-29 Yavar Kian

We consider inverse problems for a Westervelt equation with a strong damping and a time-dependent potential $q$. We first prove that all boundary measurements, including the initial data, final data, and the lateral boundary measurements,…

Analysis of PDEs · Mathematics 2023-09-22 Li Li , Yang Zhang

We show that the knowledge of the Dirichlet-to-Neumann map on the boundary of a bounded open set in $\mathbb R^n$, $n\ge 3$, for the perturbed polyharmonic operator $(-\Delta)^m+A\cdot D+q$, $m\ge 2$, with $n>m$, $A\in…

Analysis of PDEs · Mathematics 2017-03-07 Yernat M. Assylbekov

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schr\"odinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery…

Analysis of PDEs · Mathematics 2017-09-08 Yavar Kian

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex…

Mathematical Physics · Physics 2015-06-26 Hyeonbae Kang , Gen Nakamura

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Analysis of PDEs · Mathematics 2022-03-30 Li Li

We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schr\"odinger operator can be recovered H\"older stably from the boundary spectral data. This…

Analysis of PDEs · Mathematics 2025-07-21 Boya Liu , Hadrian Quan , Teemu Saksala , Lili Yan

In this article, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of…

Analysis of PDEs · Mathematics 2016-06-29 Youssef Mejri

We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$ containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. We prove that the…

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

In this paper, we introduce an inverse problem of a Schr\"odinger type variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, for $0<s<1$. We determine the unknown bounded potential $q$ from the exterior partial…

Analysis of PDEs · Mathematics 2017-08-24 Tuhin Ghosh , Yi-Hsuan Lin , Jingni Xiao

The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…

Analysis of PDEs · Mathematics 2026-01-06 Philipp Zimmermann