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In this paper we propose a domain sampling type reconstruction scheme for an inverse boundary value problem to identify an unknown cavity by single measurement on the accessible boundary of a known electric or heat conductive medium. Here…

Analysis of PDEs · Mathematics 2019-04-03 Yi-Hsuan Lin , Gen Nakamura , Haibing Wang

In this paper, we develop a factorization method to reconstruct cavities in a heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this conductor. The factorization method is a very well known reconstruction method for…

Mathematical Physics · Physics 2019-12-30 Jun Guo , Gen Nakamura , Haibing Wang

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a…

Mathematical Physics · Physics 2015-06-03 Horst Heck , Gen Nakamura , Haibing Wang

We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove…

Analysis of PDEs · Mathematics 2011-07-27 V. Bacchelli , M. Di Cristo , E. Sincich , S. Vessella

Thermal properties of a two-layered composite conductor are modified in case the interface is damaged. The present paper deals with nondestructive evaluation of perturbations of interface thermal conductance due to the presence of defects.…

Mathematical Physics · Physics 2026-05-13 Gabriele Inglese , Raffaele Inglese

Let $\Omega_\epsilon$ be a metallic plate whose top inaccessible surface has been damaged by some chemical or mechanical agent. We heat the opposite side and collect a sequence of temperature maps $u^\epsilon$. Here, we construct a formal…

Instrumentation and Detectors · Physics 2017-03-16 G. Inglese , R. Olmi , S. Priori

We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data…

Analysis of PDEs · Mathematics 2026-05-08 David Johansson

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

This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…

Numerical Analysis · Mathematics 2024-04-09 Lekbir Afraites , Julius Fergy Tiongson Rabago

We revisit the problem of identifying an unknown portion of a boundary subject to a Robin condition based on a pair of Cauchy data on the accessible part of the boundary. It is known that a single measurement may correspond to infinitely…

Numerical Analysis · Mathematics 2026-05-14 Mustapha Essahraoui , El Mehdi Cherrat , Lekbir Afraites , Julius Fergy Tiongson Rabago

In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we…

Analysis of PDEs · Mathematics 2022-08-09 Elena Beretta , M. Cristina Cerutti , Dario Pierotti , Luca Ratti

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…

Analysis of PDEs · Mathematics 2020-02-24 Chifaa Ghanmi , Saloua Mani-Aouadi , Faouzi Triki

We consider an inverse shape problem coming from electrical impedance tomography with a generalized Robin transmission condition. We will derive an algorithm in order to detect whether two materials that should be in contact are separated…

Analysis of PDEs · Mathematics 2023-11-03 Govanni Granados , Isaac Harris , Heejin Lee

We consider an inverse shape problem arising in electrical impedance tomography (EIT) for nondestructive testing, in which interior defects are modeled through Robin transmission conditions. Unlike classical formulations, we impose Robin…

Numerical Analysis · Mathematics 2026-01-19 Rafael Ceja Ayala , Malena I. Español , Govanni Granados

We deal with a boundary detection problem arising in nondestructive testing of materials. The problem consists in recovering an unknown portion of the boundary, where a Robin condition is satisfied, with the use of a Cauchy data pair…

Numerical Analysis · Mathematics 2013-05-07 Hui Cao , Sergei V. Pereverzev , Eva Sincich

The enclosure method was originally introduced for inverse problems of concerning non-destructive evaluation governed by elliptic equations. It was developed as one of useful approaches in inverse problems and applied for various equations.…

Analysis of PDEs · Mathematics 2021-03-30 Masaru Ikehata , Mishio Kawashita

A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…

Statistics Theory · Mathematics 2020-02-19 Hajime Kawakami

We prove the existence and uniqueness of the Robin heat kernel on compact Riemannian manifolds with smooth boundary for Robin parameter $\alpha\in\mathbb{R}$, expressed as a spectral expansion in terms of Robin eigenvalues and…

Analysis of PDEs · Mathematics 2025-06-19 Yifeng Meng , Kui Wang

The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…

Numerical Analysis · Mathematics 2011-09-28 Samuli Siltanen , Janne P. Tamminen

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
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