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We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…

Computer Vision and Pattern Recognition · Computer Science 2026-02-11 Joe-Mei Feng , Hsin-Hsiung Kao

The aim of the paper is to establish optimal stability estimates for the determination of sound-hard polyhedral scatterers in $\mathbb{R}^N$, $N \geq 2$, by a minimal number of far-field measurements. This work is a significant and highly…

Analysis of PDEs · Mathematics 2017-02-14 Hongyu Liu , Michele Petrini , Luca Rondi , Jingni Xiao

In this paper we prove stability results for the homology of the mapping class group of a surface. We get a stability range that is near optimal, and extend the result to twisted coefficients.

Algebraic Topology · Mathematics 2009-04-22 Søren K. Boldsen

In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…

Analysis of PDEs · Mathematics 2022-02-24 Hongyu Liu , Chun-Hsiang Tsou

We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…

Analysis of PDEs · Mathematics 2017-05-24 Hongyu Liu , Xiaodong Liu

We obtain stability estimates (with explicit constants) for the near field from the far field of a radiating solution of the Helmholtz equation. These estimates are based on new bounds for Hankel functions and quantify increasing stability…

Analysis of PDEs · Mathematics 2013-12-31 Victor Isakov

We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…

Analysis of PDEs · Mathematics 2026-05-01 Matti Lassas , Shiqi Ma , Lauri Oksanen , Mikko Salo , Jian Zhai

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

Spectral Theory · Mathematics 2023-09-11 Natalia P. Bondarenko

In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$…

Mathematical Physics · Physics 2013-08-08 Ru-Yu Lai

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…

Optics · Physics 2015-05-14 Guillaume Bal , John C Schotland

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal…

Analysis of PDEs · Mathematics 2016-02-17 Giovanni Alessandrini , Antonino Morassi , Edi Rosset , Sergio Vessella

In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an…

Optimization and Control · Mathematics 2016-08-16 Jean-Luc Gouzé , Olivier Bernard , Ludovic Mailleret

In this paper we consider the inverse scattering problem for the Schr{\"o}dinger operator with short-range electric potential. We prove in dimension n $\geq$ 2 that the knowledge of the scattering operator determines the electric potential…

Analysis of PDEs · Mathematics 2018-09-07 Luc Robbiano , Mourad Bellassoued

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…

Analysis of PDEs · Mathematics 2009-12-09 xiaodong Liu , Bo Zhang

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2020-02-19 Rakesh , Mikko Salo

In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the…

Optimization and Control · Mathematics 2015-05-30 Qi Lu

In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of…

Numerical Analysis · Mathematics 2023-04-25 Ilya Boykov , Vladimir Roudnev , Alla Boykova

We study the inverse scattering from a screen with using only one incoming time--harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the 2D--case i.e. (inverse) scattering from an…

Analysis of PDEs · Mathematics 2024-09-05 Emilia Blåsten , Petri Ola , Lassi Päivärinta

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…

Numerical Analysis · Mathematics 2020-08-13 Gang Bao , Yiwen Lin , Xiang Xu

Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…

Dynamical Systems · Mathematics 2020-08-18 Desheng Li , Qiang Liu , Xuewei Ju