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In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…

Analysis of PDEs · Mathematics 2007-05-23 Francois James , Simona Mancini , Francois Bouchut

We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…

Mathematical Physics · Physics 2015-06-03 Liliana Borcea , Fernando Guevara Vasquez , Alexander V. Mamonov

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. Our proof is based on the Schwarz…

Analysis of PDEs · Mathematics 2020-09-11 Guang-Hui Hu , Manmohan Vashisth

This works deals with one dimensional infinite perturbation - namely line defects - in periodic media. In optics, such defects are created to construct an (open) waveguide that concentrates light. The existence and the computation of the…

Spectral Theory · Mathematics 2013-01-31 Sonia Fliss

We study the non-linear Dirichlet-to-Neumann map for the Poincar\'e-Einstein filling problem. For even dimensional manifolds the range of this non-local map is described in terms of a rank two "Dirichlet-to Neumann tensor" along the…

Differential Geometry · Mathematics 2025-10-27 Samuel Blitz , A. Rod Gover , Jarosław Kopiński , Andrew Waldron

In this note, we study Calder\'on's problem for certain classes of conductivities in domains with circular symmetry in two and three dimensions. Explicit formulas are obtained for the reconstruction of the conductivity from the…

Analysis of PDEs · Mathematics 2019-03-19 Mai Thi Kim Dung , Dang Anh Tuan

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…

Analysis of PDEs · Mathematics 2020-09-25 W. Rundell , M. Yamamoto

We analyze the inverse problem of recovering geometric information from the return map induced by a round-trip between a convex core C and an admissible domain. This process defines a discrete dynamical system on the boundary of C governed…

Dynamical Systems · Mathematics 2026-04-29 Mohamed El Morsalani , Mohammed Barkatou

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…

Analysis of PDEs · Mathematics 2024-11-05 Sebastián Muñoz-Thon

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of…

Analysis of PDEs · Mathematics 2019-01-23 Tommi Brander , Bastian von Harrach , Manas Kar , Mikko Salo

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

Analysis of PDEs · Mathematics 2023-04-06 Pu-Zhao Kow , Yi-Hsuan Lin , Jenn-Nan Wang

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…

Numerical Analysis · Mathematics 2012-10-30 Adriano De Cezaro , B. Tomas Johansson

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…

High Energy Physics - Theory · Physics 2017-04-06 S. Teber , A. V. Kotikov

In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…

Analysis of PDEs · Mathematics 2026-04-09 Ravi Shankar Jaiswal , Pu-Zhao Kow , Suman Kumar Sahoo

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

This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…

Analysis of PDEs · Mathematics 2019-12-12 Masaru Ikehata

We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…

Analysis of PDEs · Mathematics 2024-09-05 Emilia Blåsten , Petri Ola , Lassi Päivärinta

Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove…

Numerical Analysis · Mathematics 2025-07-08 Xiaodong Liu , Jiguang Sun , Lei Zhang

We consider the inverse problem to determine a smooth compact Riemannian manifold with boundary $(M, g)$ from a restriction $\Lambda_{\Src, \Rec}$ of the Dirichlet-to-Neumann operator for the wave equation on the manifold. Here $\Src$ and…

Analysis of PDEs · Mathematics 2015-01-14 Matti Lassas , Lauri Oksanen