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A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.

Analysis of PDEs · Mathematics 2011-11-10 Katsiaryna Krupchyk , Matti Lassas

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…

Functional Analysis · Mathematics 2007-05-23 Paolo Dall'Aglio

An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…

Mathematical Physics · Physics 2007-05-23 H. Ammari , A. G. Ramm

This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…

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

We study the existence, uniqueness, and regularity of weak solutions to a class of obstacle problems, where the obstacle condition can be imposed on a subset of the domain. In particular, we establish the optimal H\"older regularity for…

Analysis of PDEs · Mathematics 2025-01-28 Ki-Ahm Lee , Se-Chan Lee , Waldemar Schefer

We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…

Analysis of PDEs · Mathematics 2019-12-09 Kaïs Ammari , Mourad Choulli , Faouzi Triki

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…

Analysis of PDEs · Mathematics 2021-04-29 Jiaqing Yang

The boundary problem is considered for inhomogeneous increasing random walks on the square lattice ${\mathbb Z}_+^2$ with weighted edges. Explicit solutions are given for some instances related to the classical and generalized number…

Probability · Mathematics 2009-09-29 Alexander Gnedin

This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…

Analysis of PDEs · Mathematics 2023-01-20 Yixian Gao , Hongyu Liu , Yang Liu

We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.

Analysis of PDEs · Mathematics 2007-05-23 Eva Sincich

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…

Analysis of PDEs · Mathematics 2019-01-11 Giovanni Covi

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

Numerical Analysis · Mathematics 2023-10-13 Yan Chang , Yukun Guo , Hongyu Liu , Deyue Zhang

We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then…

Exactly Solvable and Integrable Systems · Physics 2014-11-04 Luis C. García-Naranjo , Andrzej J. Maciejewski , Juan C. Marrero , Maria Przybylska

Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use…

Analysis of PDEs · Mathematics 2023-06-28 Gyeongha Hwang , Manas Kar

It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…

Analysis of PDEs · Mathematics 2023-03-15 Yue Zhao

For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23--50). In particular at singular points we introduce a…

Analysis of PDEs · Mathematics 2017-08-08 Maria Colombo , Luca Spolaor , Bozhidar Velichkov

We first formulate an inverse problem for a linear fractional Lam\'e system. We determine the Lam\'e parameters from exterior partial measurements of the Dirichlet-to-Neumann map. We further study an inverse obstacle problem as well as an…

Analysis of PDEs · Mathematics 2021-09-09 Li Li

This paper investigates a shape optimization problem involving the Signorini unilateral conditions in a linear elastic model, without any penalization procedure. The shape sensitivity analysis is performed using tools from convex and…

Optimization and Control · Mathematics 2025-02-25 Aymeric Jacob de Cordemoy