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In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…

Analysis of PDEs · Mathematics 2016-05-09 Adrian Nachman , Alexandru Tamasan , Johann Veras

We propose an alternative proof of the classical result of Type-I blowup with log correction for the semilinear heat equation. Compared with previous proofs, we use a novel idea of enforcing stable normalizations for perturbations around…

Analysis of PDEs · Mathematics 2026-01-14 Thomas Y. Hou , Van Tien Nguyen , Yixuan Wang

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{\"o}lder stability with…

Analysis of PDEs · Mathematics 2015-01-08 Michel Cristofol , Shumin Li , Eric Soccorsi

In this paper, we mainly study error bounds for a single convex inequality and semi-infinite convex constraint systems, and give characterizations of stability of error bounds via directional derivatives. For a single convex inequality, it…

Optimization and Control · Mathematics 2024-01-11 Zhou Wei , Michel Thera , Jen-Chih Yao

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

Algebraic Topology · Mathematics 2016-02-25 Moritz Groth

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 introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve…

Signal Processing · Electrical Eng. & Systems 2020-01-08 Qing Zou , Sunrita Poddar , Mathews Jacob

In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\sigma|\nabla u|^p$, $0 < p \leq 1$, where $u$ is the solution of the…

Analysis of PDEs · Mathematics 2015-06-16 Carlos Montalto , Plamen Stefanov

We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…

Analysis of PDEs · Mathematics 2021-12-23 Alessandro Felisi , Luca Rondi

On a Riemannian manifold $(M, g)$ with Anosov geodesic flow, the problem of recovering a connection from the knowledge of traces of its holonomies along primitive closed geodesics is known as the holonomy inverse problem. In this paper, we…

Analysis of PDEs · Mathematics 2024-04-23 Mihajlo Cekić , Thibault Lefeuvre

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

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…

Systems and Control · Computer Science 2012-06-05 Corentin Briat

We address the stability issue in Calder\'on's problem for a special class of anisotropic conductivities of the form $\sigma=\gamma A$ in a Lipschitz domain $\Omega\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous…

Analysis of PDEs · Mathematics 2024-08-08 Sonia Foschiatti , Romina Gaburro , Eva Sincich

Consider a parameter dependent vector field on either Euclidean space or a compact Riemannian manifold. Suppose that it possesses a parameter dependent initial condition and a parameter dependent stable hyperbolic equilibrium point. It is…

Dynamical Systems · Mathematics 2020-10-08 Michael W. Fisher , Ian A. Hiskens

We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…

Analysis of PDEs · Mathematics 2026-04-21 Kui Ren , Yimin Zhong

In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional…

Analysis of PDEs · Mathematics 2021-12-08 D. Baidiuk , L. Paunonen

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

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…

Analysis of PDEs · Mathematics 2023-06-13 Mourad Choulli

In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows…

Analysis of PDEs · Mathematics 2022-06-13 Bian Wu