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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

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

In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on a part of the boundary, a problem that commonly arises in…

Numerical Analysis · Mathematics 2025-06-10 Erik Burman , Siyu Cen , Bangti Jin , Zhi Zhou

We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the…

Analysis of PDEs · Mathematics 2020-07-08 Matteo Santacesaria , Toshiaki Yachimura

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube…

General Relativity and Quantum Cosmology · Physics 2007-05-23 N. Bishop , R. Gomez , L. Lehner , J. Winicour

We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…

Analysis of PDEs · Mathematics 2024-09-05 Isaac Harris , Andreas Kleefeld , Heejin Lee

In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…

Analysis of PDEs · Mathematics 2015-03-30 Sebastian Acosta

Active thermography is a non-destructive testing technique to detect the internal structure of a heat conductor, which is widely applied in industrial engineering. In this paper, we consider the problem of identifying an unknown cavity with…

Mathematical Physics · Physics 2015-05-25 Gen Nakamura , Haibing Wang

We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem…

Optimization and Control · Mathematics 2022-01-05 Ruanui Nicholson , Matti Niskanen

A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…

Optimization and Control · Mathematics 2024-03-19 Julius Fergy Tiongson Rabago , Lekbir Afraites , Hirofumi Notsu

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

Numerical Analysis · Mathematics 2026-01-27 Manabu Machida , Hirofumi Notsu , Julius Fergy Tiongson Rabago

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

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…

Analysis of PDEs · Mathematics 2017-03-08 Elena Beretta , Andrea Manzoni , Luca Ratti

We consider a boundary-value problem for the second order elliptic differential operator with rapidly oscillating coefficients in a domain $\Omega_{\epsilon}$ that is $\epsilon-$periodically perforated by small holes. The holes are divided…

Analysis of PDEs · Mathematics 2008-06-16 Taras A. Mel'nyk , Olena A. Sivak

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

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

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

In this paper, we address a classical case of the Calder\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\omega$ (with boundary $\gamma$) contained in a domain…

Analysis of PDEs · Mathematics 2015-09-10 Alexandre Munnier , Karim Ramdani

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…

Mathematical Physics · Physics 2020-07-14 Christian Daveau , Abdessatar Khelifi , Houssem Lihiou

For a wave equation with time-independent Lorentzian metric consider an initial-boundary value problem in $\mathbb{R}\times \Omega$, where $x_0\in \mathbb{R}$, is the time variable and $\Omega$ is a bounded domain in $\mathbb{R}^n$. Let…

Analysis of PDEs · Mathematics 2024-03-04 Gregory Eskin
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