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In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…

Analysis of PDEs · Mathematics 2014-07-22 Lucie Baudouin , Masahiro Yamamoto

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…

Analysis of PDEs · Mathematics 2019-11-04 Chan Liu , Jin Wen , Zhidong Zhang

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 are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Analysis of PDEs · Mathematics 2017-06-15 Jingzhi Li , Xiaofei Li , Hongyu Liu

We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , Leonidas Mindrinos

This article addresses the inverse problem of simultaneously recovering both the wave speed coefficient and an unknown initial condition (acting as the source) for the multidimensional wave equation from a single passive boundary…

Analysis of PDEs · Mathematics 2025-07-29 Yavar Kian , Hongyu Liu

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…

Geophysics · Physics 2022-05-19 Xin Zhang , Muhammad Atif Nawaz , Xuebin Zhao , Andrew Curtis

In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…

Analysis of PDEs · Mathematics 2020-12-07 Gen Nakamura , Manmohan Vashisth , Michiyuki Watanabe

In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…

Analysis of PDEs · Mathematics 2022-12-08 Song-Ren Fu

We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear…

Solar and Stellar Astrophysics · Physics 2017-07-28 Laurent Gizon , Damien Fournier , Thorsten Hohage

Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…

Mathematical Physics · Physics 2023-01-13 Evgeny Korotyaev

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…

Analysis of PDEs · Mathematics 2015-08-10 Lung-Hui Chen

This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…

Analysis of PDEs · Mathematics 2022-06-14 Chiun-Chang Lee , Masashi Mizuno , Sang-Hyuck Moon

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

Analysis of PDEs · Mathematics 2023-07-06 Kui Ren , Nathan Soedjak

We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…

Numerical Analysis · Mathematics 2023-02-14 Bastian Harrach , Tim Jahn , Roland Potthast

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

Optics · Physics 2012-08-23 Johannes Skaar , Magnus W. Haakestad

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

Complex Variables · Mathematics 2020-08-19 Mohamed M S Nasser , Matti Vuorinen

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

Differential Geometry · Mathematics 2018-05-09 María Barbero-Liñán , Marta Farré Puiggalí , Sebastián Ferraro , David Martín de Diego

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…

Analysis of PDEs · Mathematics 2015-10-01 Kais Ammari , Mourad Choulli , Faouzi Triki