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We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Romina Gaburro

In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…

Analysis of PDEs · Mathematics 2014-12-04 Pedro Caro , Valter Pohjola

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

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 consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Analysis of PDEs · Mathematics 2022-03-18 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary…

Mathematical Physics · Physics 2009-11-11 A. S. Fokas , B. Pelloni

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

Analysis of PDEs · Mathematics 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

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

We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…

Analysis of PDEs · Mathematics 2020-11-13 Yavar Kian , Gunther Uhlmann

We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…

Analysis of PDEs · Mathematics 2023-03-22 Lei Zhang , Yue Zhao

In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schr\"odinger operator in dimension $n\geq 3$. We assume that the inaccessible part of the boundary is part of a…

Analysis of PDEs · Mathematics 2016-10-17 Leyter Potenciano-Machado

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\Omega$ in $\R^n, n\geq 2$. We recover the coefficients at the boundary from the…

Analysis of PDEs · Mathematics 2024-01-12 Nitesh Kumar , Tanmay Sarkar , Manmohan Vashisth

We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a two-plane is determined by the…

Analysis of PDEs · Mathematics 2007-05-23 Allan Greenleaf , Gunther Uhlmann

In this study, we consider two nonlinear Schr\"{o}dinger-type models that are derived by R L. Frank, F. M\'{e}hats, C. Sparber [arXiv:1611.01574] to study 3D nonlinear Schr\"{o}dinger equations under strong magnetic fields. One model is…

Analysis of PDEs · Mathematics 2024-11-06 Jumpei Kawakami

We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ \epsilon(x)\partial_t u^m-\nabla\cdot\bigl(\gamma(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{in }(0,T)\times\Omega, \] where…

Analysis of PDEs · Mathematics 2026-03-10 Cătălin I. Cârstea , Tuhin Ghosh

We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…

Mathematical Physics · Physics 2011-11-11 S. A. Avdonin , V. S. Mikhaylov , K. Ramdani

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

Analysis of PDEs · Mathematics 2023-04-25 Xiaomeng Zhao , Ganghua Yuan

We deal with two dynamical systems associated with a Riemannian manifold with boundary. The first one is a system governed by the scalar wave equation, the second is governed by the Maxwell equations. Both of the systems are controlled from…

Mathematical Physics · Physics 2015-06-19 M. I. Belishev , M. N. Demchenko

The aim of this paper is to study a nonlocal problem with a mixed Dirichlet-Neumann exterior condition. We prove existence, nonexistence and multiplicity of positive energy solutions and describe the interaction between the concave-convex…

Analysis of PDEs · Mathematics 2016-12-22 Boumediene Abdellaoui , Abdelrazek Dieb , Enrico Valdinoci

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2019-01-15 Gen Nakamura , Manmohan Vashisth
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