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We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of…

Analysis of PDEs · Mathematics 2014-04-16 Giovanni Alessandrini , Eva Sincich , Sergio Vessella

We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the…

Analysis of PDEs · Mathematics 2010-04-14 Eva Sincich

We establish a logarithmic stability estimate for the problem of detecting corrosion by a single electric measurement. We give a proof based on an adaptation of the method initiated in \cite{BCJ} for solving the inverse problem of…

Analysis of PDEs · Mathematics 2015-09-23 Mourad Choulli , Aymen Jbalia

We deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one.

Analysis of PDEs · Mathematics 2007-05-23 Giovanni Alessandrini , Eva Sincich

We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Furthermore, we demonstrate how the stability inequalities derived…

Analysis of PDEs · Mathematics 2025-11-14 Mourad Choulli , Shuai Lu , Hiroshi Takase

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain…

Analysis of PDEs · Mathematics 2015-05-18 Andrea Ballerini

In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…

Numerical Analysis · Mathematics 2019-04-08 Bastian Harrach , Houcine Meftahi

We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…

Analysis of PDEs · Mathematics 2014-04-16 Giovanni Alessandrini , Kyoungsun Kim

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

Analysis of PDEs · Mathematics 2019-02-13 Hongyu Liu , Chun-Hsiang Tsou

We deal with the problem of determining an inclusion within an electrical conductor from electrical boundary measurements. Under mild a priori assumptions we establish an optimal stability estimate.

Analysis of PDEs · Mathematics 2007-05-23 Giovanni Alessandrini , Michele Di Cristo

We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local…

Analysis of PDEs · Mathematics 2022-07-07 Andrea Aspri , Elena Beretta , Elisa Francini , Sergio Vessella

This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.

Analysis of PDEs · Mathematics 2026-05-12 Tianrui Dai

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the…

Analysis of PDEs · Mathematics 2011-07-28 Andrea Ballerini

We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

Analysis of PDEs · Mathematics 2024-09-10 Giovanni Covi , Jesse Railo , Teemu Tyni , Philipp Zimmermann

We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^2$ norm when the data of the Calder\'on Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are…

Analysis of PDEs · Mathematics 2022-02-03 Daniel Faraco , Martí Prats

We continue our study, started in arXiv:2212.00705, of (self-)collisions of viscoelastic solids in an inertial regime. We show existence of weak solutions with a corresponding contact force measure in the case of solids with only…

Analysis of PDEs · Mathematics 2023-12-04 Antonín Češík , Giovanni Gravina , Malte Kampschulte

We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…

Analysis of PDEs · Mathematics 2023-05-16 Huaian Diao , Hongyu Liu , Longyue Tao

We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz…

Analysis of PDEs · Mathematics 2025-07-30 Pedro Caro , María Ángeles García-Ferrero , Keith M. Rogers

In this brief note, we establish a novel criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the presence of possibly unbounded perturbations (external disturbances). To prove the result,…

Dynamical Systems · Mathematics 2021-01-05 Robert Vrabel

We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…

Analysis of PDEs · Mathematics 2021-12-30 Mourad Choulli
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