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In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…

Analysis of PDEs · Mathematics 2024-04-23 Hongyu Liu , Catharine W. K. Lo

The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…

Analysis of PDEs · Mathematics 2018-01-08 Yaroslav Kurylev , Matti Lassas , Lauri Oksanen , Gunther Uhlmann

We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…

Analysis of PDEs · Mathematics 2025-03-14 Mourad Choulli , Hiroshi Takase

We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…

Analysis of PDEs · Mathematics 2011-06-17 Lauri Oksanen

We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…

Functional Analysis · Mathematics 2007-05-23 P. Dall'Aglio , C. Leone

The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…

High Energy Physics - Lattice · Physics 2023-03-01 Alessandro Candido , Luigi Del Debbio , Tommaso Giani , Giacomo Petrillo

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…

Analysis of PDEs · Mathematics 2014-05-13 David Dos Santos Ferreira , Yaroslav Kurylev , Matti Lassas , Mikko Salo

In this article we study the inverse problem of determining a semilinear term appearing in an elliptic equation from boundary measurements. Our main objective is to develop flexible and general theoretical results that can be used for…

Numerical Analysis · Mathematics 2024-11-18 Yavar Kian , Hongyu Liu , Li-Li Wang , Guang-Hui Zheng

In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is…

Analysis of PDEs · Mathematics 2026-05-05 Paolo Piersanti

In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the…

Differential Geometry · Mathematics 2015-07-28 Arif Amirov , Fikret Gölgeleyen , Masahiro Yamamoto

We prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate…

Analysis of PDEs · Mathematics 2015-02-27 Matteo Focardi , Emanuele Spadaro

We are concerned with the inverse boundary problem of determining anomalies associated with a semilinear elliptic equation of the form $-\Delta u+a(\mathbf x, u)=0$, where $a(\mathbf x, u)$ is a general nonlinear term that belongs to a…

Analysis of PDEs · Mathematics 2022-07-25 Huaian Diao , Xiaoxu Fei , Hongyu Liu , Li Wang

An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…

Mathematical Physics · Physics 2009-10-31 A. G. Ramm

We determine the twist in a birefringent optical fiber from measurements, at one end of the fiber, of the fiber response to an impulsive source at the same end. This is the inverse problem of determining a non-constant coefficient, of a…

Analysis of PDEs · Mathematics 2015-12-09 Rakesh , Jiahua Tang , Andrew A Lacey

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…

Analysis of PDEs · Mathematics 2020-05-20 Antonios Charalambopoulos , Vanessa Markaki , Drosos Kourounis

In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lam\'e system. Relying on an observation by Schumann \cite{Schumann1}, we reduce the question of the solution's and the free…

Analysis of PDEs · Mathematics 2021-01-05 Angkana Rüland , Wenhui Shi

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…

Analysis of PDEs · Mathematics 2017-02-14 Luca Rondi , Fadil Santosa

To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We…

Soft Condensed Matter · Physics 2009-11-10 Benjamin Dollet , Miguel Aubouy , Francois Graner

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…

Analysis of PDEs · Mathematics 2011-09-21 Masaru Ikehata