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In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…

Spectral Theory · Mathematics 2024-11-12 Xiao-Chuan Xu , Yi-Jun Pan

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

Analysis of PDEs · Mathematics 2024-02-21 Katya Krupchyk , Shiqi Ma , Suman Kumar Sahoo , Mikko Salo , Simon St-Amant

The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…

Mathematical Physics · Physics 2020-05-22 Tuncay Aktosun , Ricardo Weder

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

An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…

Mathematical Physics · Physics 2009-11-10 Tuncay Aktosun , Ricardo Weder

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…

Analysis of PDEs · Mathematics 2009-02-25 Pedro Caro , Petri Ola , Mikko Salo

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

Analysis of PDEs · Mathematics 2015-06-15 Yavar Kian , Quang Sang Phan , Eric Soccorsi

We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…

Analysis of PDEs · Mathematics 2019-03-05 Cătălin I. Cârstea , Gen Nakamura , Lauri Oksanen

We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator,…

Mathematical Physics · Physics 2017-12-12 S. A. Avdonin , S. A. Ivanov , J. M. Wang

This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some…

Analysis of PDEs · Mathematics 2011-11-30 Francis J. Chung

Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods…

Analysis of PDEs · Mathematics 2014-12-16 Peter D. Miller , Zhenyun Qin

We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…

Analysis of PDEs · Mathematics 2020-11-04 Yavar Kian , Katya Krupchyk , Gunther Uhlmann

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

Analysis of PDEs · Mathematics 2013-11-12 Yang Yang

A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…

Spectral Theory · Mathematics 2012-05-22 Jussi Behrndt , Jonathan Rohleder

The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…

Analysis of PDEs · Mathematics 2025-08-15 Mihajlo Cekić , Anna Siffert

This paper is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data…

Analysis of PDEs · Mathematics 2022-03-01 Xiaoxu Xu , Guanghui Hu , Bo Zhang , Haiwen Zhang

The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of…

Analysis of PDEs · Mathematics 2015-11-10 J. Behrndt , A. F. M. ter Elst

We study the inverse boundary problem for a nonlinear magnetic Schr\"odinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the…

Analysis of PDEs · Mathematics 2023-10-25 Katya Krupchyk , Gunther Uhlmann

This work considers properties of the Neumann-to-Dirichlet map for the conductivity equation under the assumption that the conductivity is identically one close to the boundary of the examined smooth, bounded and simply connected domain. It…

Analysis of PDEs · Mathematics 2012-04-03 Nuutti Hyvönen , Petteri Piiroinen , Otto Seiskari