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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

This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

Analysis of PDEs · Mathematics 2024-08-01 Adel Blouza , Léo Glangetas , Yavar Kian , Van-Sang Ngo

A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…

Strongly Correlated Electrons · Physics 2023-01-23 Avi Shragai , Florian Theuss , Gael Grissonnanche , B. J. Ramshaw

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…

Analysis of PDEs · Mathematics 2009-02-25 Pedro Caro , Petri Ola , Mikko Salo

The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are…

Metric Geometry · Mathematics 2024-02-09 Beniamin Bogosel

The recovery of anomalies from backscattering far field data is a long-standing open problem in inverse scattering theory. We make a first step in this direction by establishing the unique identifiability of convex impenetrable obstacles…

Numerical Analysis · Mathematics 2025-12-29 Jialei Li , Xiaodong Liu , Qingxiang Shi

The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…

Differential Geometry · Mathematics 2016-03-27 María Barbero-Liñán , Marta Farré Puiggalí , David Martín de Diego

In this paper, we investigate the inverse Stokes problem of determining a discontinuous viscosity coefficient $\mu$ in a bounded domain $\Omega\subset\mathbb{R}^3$. By analyzing the singularity of the Dirichlet Green's functions in…

Analysis of PDEs · Mathematics 2025-11-25 Yu Jia , Chengyu Wu , Hao Wu , Jiaqing Yang

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…

Analysis of PDEs · Mathematics 2021-04-27 Ru-Yu Lai , Hanming Zhou

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

Mathematical Physics · Physics 2015-06-12 M. Fedele , C. Vernia , P. Contucci

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…

Analysis of PDEs · Mathematics 2025-12-04 Chun Liu , Jiaqing Yang , Bo Zhang

We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…

Analysis of PDEs · Mathematics 2019-03-11 Pedro Caro , Ru-Yu Lai , Yi-Hsuan Lin , Ting Zhou

We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem…

Analysis of PDEs · Mathematics 2015-07-24 Tomasz Klimsiak , Andrzej Rozkosz

This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and…

Optimization and Control · Mathematics 2024-10-16 Samir Adly , Loïc Bourdin , Fabien Caubet , Aymeric Jacob de Cordemoy

The problem of interest in this article is to study the (nonlocal) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schr\"{o}dinger equation. Let $0<a<1$, and $u$ solves…

Analysis of PDEs · Mathematics 2020-11-16 Tuhin Ghosh

The aim of this chapter is to make a review of the recent results using the Enclosure Method on inverse obstacle problems governed by the wave equation and the Maxwell system in time domain. We also describe some of unsolved problems…

Analysis of PDEs · Mathematics 2015-12-16 Masaru Ikehata

In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…

Analysis of PDEs · Mathematics 2026-05-19 Chun-Hsiang Tsou

In this paper, we give a positive answer to a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far…

Analysis of PDEs · Mathematics 2021-04-20 Genqian Liu

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…

Analysis of PDEs · Mathematics 2020-01-27 Masaru Ikehata

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov