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We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

Analysis of PDEs · Mathematics 2007-05-23 Alexander Katchalov , Yaroslav Kurylev , Matti Lassas , Niculae Mandache

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

Analysis of PDEs · Mathematics 2023-04-06 Pu-Zhao Kow , Yi-Hsuan Lin , Jenn-Nan Wang

This paper is devoted to the uniqueness in inverse acoustic scattering problems for the Helmholtz equation with phaseless far-field data. Some novel techniques are developed to overcome the difficulty of translation invariance induced by a…

Analysis of PDEs · Mathematics 2018-07-04 Deyue Zhang , Yukun Guo

We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial…

Data Structures and Algorithms · Computer Science 2014-01-17 Kamen M. Lozev

In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensional interior acoustic wave equation coupled to a Kirchoff…

Analysis of PDEs · Mathematics 2010-10-14 Shitao Liu

We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by…

Analysis of PDEs · Mathematics 2025-03-19 Shitao Liu , Antonio Pierrottet

We consider the stability in the inverse problem consisting of the determination of a time-dependent coefficient of order zero $q$, appearing in a Dirichlet initial-boundary value problem for a wave equation $\partial_t^2u-\Delta…

Analysis of PDEs · Mathematics 2016-02-01 Yavar Kian

We found a simple procedure for the solution of the time - independent Schrodinger equation in one dimension without making any approximation. The wave functions are always periodic. Two difficulties may be encountered: one is to solve the…

Quantum Physics · Physics 2007-05-23 H. H. Erbil

We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…

Analysis of PDEs · Mathematics 2022-08-11 Li Li

A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field,…

Numerical Analysis · Mathematics 2022-03-30 Anatoly B. Bakushinsky , Alexander S. Leonov

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 article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…

Analysis of PDEs · Mathematics 2021-05-26 Yavar Kian , Yikan Liu , Masahiro Yamamoto

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed…

Analysis of PDEs · Mathematics 2024-11-26 Mourad Choulli , Hiroshi Takase

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…

Analysis of PDEs · Mathematics 2020-03-25 Tuhin Ghosh , Mikko Salo , Gunther Uhlmann

We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…

Analysis of PDEs · Mathematics 2009-11-11 Mikko Salo , Jenn-Nan Wang

In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…

Numerical Analysis · Mathematics 2024-10-04 Jérémy Heleine

This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…

Analysis of PDEs · Mathematics 2019-02-20 Guanghui Hu , Long Li , Jun Zou

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

This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…

Mathematical Physics · Physics 2012-06-14 Peter C. Gibson

We study two new classes of inverse problems for a time-switched system in which a fractional wave equation (with Caputo derivative of order $\alpha \in (1,2)$) governs the dynamics on the interval $[0,a)$, and a fractional diffusion…

Analysis of PDEs · Mathematics 2026-05-26 E. T. Karimov , N. A. Murolimova