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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

Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral…

Analysis of PDEs · Mathematics 2022-02-08 Muhammad Ali , Sara Aziz

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

Mathematical Physics · Physics 2009-12-03 Andrea A. Almasy

A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The…

Numerical Analysis · Mathematics 2025-02-19 Vladislav V. Kravchenko , Sergii M. Torba , Alexander O. Vatulyan

The matrix Sturm-Liouville operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm-Liouville operators on geometrical graphs.…

Spectral Theory · Mathematics 2020-07-16 Natalia P. Bondarenko

As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with determining the adequate orders of time-fractional…

Analysis of PDEs · Mathematics 2021-07-21 Ravshan Ashurov , Sabir Umarov

The perturbation of the Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions by a convolution operator is considered. Local stability and global unique solvability of the inverse problem of recovering the…

Spectral Theory · Mathematics 2020-02-04 Sergey Buterin

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 develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analysis and submarine underwater radar…

Classical Analysis and ODEs · Mathematics 2025-06-27 Yuchao He , Mengda Wu , Yonghui Xia , Meirong Zhang

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…

Analysis of PDEs · Mathematics 2018-06-12 Mourad Choulli , Faouzi Triki

Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…

Analysis of PDEs · Mathematics 2022-04-06 Jiaqing Yang , Jianliang Li , Bo Zhang

Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…

Analysis of PDEs · Mathematics 2024-11-12 Hjørdis Schlüter

The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…

Numerical Analysis · Mathematics 2021-05-26 Long Li , Jiansheng Yang , Bo Zhang , Haiwen Zhang

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of…

Spectral Theory · Mathematics 2016-09-13 O. P. Boyko , O. M. Martynyuk , V. N. Pivovarchik

We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…

Analysis of PDEs · Mathematics 2025-01-14 Manuel Cañizares

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan

We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…

Spectral Theory · Mathematics 2015-10-02 Vjacheslav Yurko

The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…

Spectral Theory · Mathematics 2018-05-22 Tuncay Aktosun , Vassilis G. Papanicolaou

An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the…

Spectral Theory · Mathematics 2020-03-05 Natalia Bondarenko

A connection, which shows the dependence of norming constants on boundary conditions, was found using the Gelfand-Levitan method for the solution of inverse Sturm-Liouville problem.

Spectral Theory · Mathematics 2017-05-19 Yuri Ashrafyan , Tigran Harutunyan