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We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…

Numerical Analysis · Mathematics 2017-10-06 Pavel Bochev , James Cheung , Max Gunzburger , Mauro Perego

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte…

Computational Engineering, Finance, and Science · Computer Science 2022-06-20 Julien Berger , Clemence Legros

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

Analysis of PDEs · Mathematics 2022-03-18 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…

Numerical Analysis · Mathematics 2015-06-12 Kazufumi Ito , Bangti Jin , Jun Zou

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

What happens when one prescribes a heat flux which is proportional to the Neumann data of a solution of the wave equation in the whole space on the surface of a heat conductive body? It is shown that there is a difference in the asymptotic…

Analysis of PDEs · Mathematics 2021-03-09 Masaru Ikehata

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…

Analysis of PDEs · Mathematics 2023-06-02 Mansur I. Ismailov , Tohru Ozawa , Durvudkhan Suragan

This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…

Analysis of PDEs · Mathematics 2025-01-22 Targyn A. Nauryz , Khumoyun Jabbarkhanov

The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.

Spectral Theory · Mathematics 2015-12-22 Natalia Bondarenko

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…

Numerical Analysis · Mathematics 2015-05-30 Bangti Jin

In this paper, we consider the inverse problem of determining the time-dependent source term in the general setting of Hilbert spaces and for general additional data. We prove the well-posedness of this inverse problem by reducing the…

Analysis of PDEs · Mathematics 2023-06-09 Daurenbek Serikbaev , Michael Ruzhansky , Niyaz Tokmagambetov

The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…

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

We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region…

Analysis of PDEs · Mathematics 2026-02-13 Elena Beretta , Elisa Francini , Dario Pierotti , Eva Sincich

We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…

Analysis of PDEs · Mathematics 2024-06-18 Ali Feizmohammadi , Yavar Kian , Lauri Oksanen

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…

Disordered Systems and Neural Networks · Physics 2009-11-11 Olivier Rivoire

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

Analysis of PDEs · Mathematics 2012-10-22 G. Giorgi , M. Brignone , R. Aramini , M. Piana

We study inverse boundary problems for the advection diffusion equation on an admissible manifold, i.e. a compact Riemannian manifold with boundary of dimension $\ge 3$, which is conformally embedded in a product of the Euclidean real line…

Analysis of PDEs · Mathematics 2017-04-20 Katya Krupchyk , Gunther Uhlmann

We examine various density results related to the solutions of the non-local heat equation at a specific time slice, focusing on two distinct models: one with homogeneous Dirichlet boundary condition and the other with singular boundary…

Analysis of PDEs · Mathematics 2025-12-30 Saumyajit Das

In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…

Analysis of PDEs · Mathematics 2019-03-15 Michael Hinze , Bernd Hofmann , Tran Nhan Tam Quyen