English
Related papers

Related papers: Linear sampling method for identifying cavities in…

200 papers

A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…

Analysis of PDEs · Mathematics 2017-08-24 Nasser Al-Salti , Mokhtar Kirane , Berikbol T. Torebek

Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads…

Numerical Analysis · Mathematics 2017-05-31 Nuutti Hyvönen , Lauri Mustonen

We consider an inverse boundary value problem for the heat equation with a nonsmooth coefficient of conductivity which models the displacement of a moving body inside a nonhomogeneous background. We prove the uniqueness of the moving…

Analysis of PDEs · Mathematics 2022-01-24 Olivier Poisson

We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , Leonidas Mindrinos

In this paper, we derive a Sampling Method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second-order…

Analysis of PDEs · Mathematics 2019-05-30 Isaac Harris

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

A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. The idea gives a design of a special heat flux on the surface…

Analysis of PDEs · Mathematics 2021-03-09 Masaru Ikehata

This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A {\it…

Analysis of PDEs · Mathematics 2015-12-03 Masaru Ikehata , Mishio Kawashita

This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…

Analysis of PDEs · Mathematics 2025-09-04 Isaac Harris , Peijun Li , General Ozochiawaeze

Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…

Analysis of PDEs · Mathematics 2020-12-15 Tielei Zhu , Jiaqing Yang

We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data"…

Numerical Analysis · Mathematics 2019-02-20 Michael V. Klibanov , Jingzhi Li , Wenlong Zhang

We consider an inverse boundary value problem for the heat equation $\partial_t v = {\rm div}_x\,(\gamma\nabla_x v)$ in $(0,T)\times\Omega$, where $\Omega$ is a bounded domain of $R^3$, the heat conductivity $\gamma(t,x)$ admits a surface…

Analysis of PDEs · Mathematics 2015-06-15 Olivier Poisson

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

Analysis of PDEs · Mathematics 2022-01-31 Michael Levitin , Peter Monk , Virginia Selgas

In this work, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann…

Numerical Analysis · Mathematics 2022-10-06 Umberto Emil Morelli , Patricia Barral , Peregrina Quintela , Gianluigi Rozza , Giovanni Stabile

In this paper we show uniqueness of the conductivity for the quasilinear Calder\'on's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions…

Analysis of PDEs · Mathematics 2018-06-26 Claudio Muñoz , 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

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

In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…

Numerical Analysis · Mathematics 2024-04-23 M. A. Botchev , V. T. Zhukov

We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…

Analysis of PDEs · Mathematics 2016-11-03 Giovanni Alessandrini , Maarten V. de Hoop , Romina Gaburro , Eva Sincich