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This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order…

Analysis of PDEs · Mathematics 2025-11-11 Tianyu Cai , Xi Chen

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

Spectral Theory · Mathematics 2019-11-25 Natalia Bondarenko , Vjacheslav Yurko

Let $L_0$ be a closed densely defined symmetric semi-bounded operator with nonzero defect indexes in a separable Hilbert space ${\cal H}$. With $L_0$ we associate a metric space $\Omega_{L_0}$ that is named a {\it wave spectrum} and…

Functional Analysis · Mathematics 2010-04-13 M. I. Belishev

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

Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…

Spectral Theory · Mathematics 2015-02-02 Vjacheslav Yurko

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

We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which…

Analysis of PDEs · Mathematics 2021-01-27 Tony Liimatainen , Lauri Oksanen

This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic…

Analysis of PDEs · Mathematics 2026-04-15 Irina Kmit , Nataliya Protsakh , Viktor Tkachenko

In this paper, we study the direct and inverse spectral problems for the Schrodinger operator with two generalized Regge boundary conditions. For the direct problem, we give the properties of the spectrum, including the asymptotic…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Yu-Ting Huang

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 Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…

Mathematical Physics · Physics 2009-11-10 Tuncay Aktosun , Ricardo Weder

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…

Analysis of PDEs · Mathematics 2025-03-25 Durdiev Durdimurod Kalandarovich

In this paper, we study the inverse scattering problem for energy-dependent Schr\"{o}dinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions,…

Spectral Theory · Mathematics 2020-07-13 Rostyslav Hryniv , Stepan Manko

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…

Analysis of PDEs · Mathematics 2011-01-26 Lauri Oksanen

In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…

Analysis of PDEs · Mathematics 2022-01-05 J. Apraiz , A. Doubova , E. Fernández-Cara , M. Yamamoto

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

Analysis of PDEs · Mathematics 2024-02-21 Katya Krupchyk , Shiqi Ma , Suman Kumar Sahoo , Mikko Salo , Simon St-Amant

This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…

Spectral Theory · Mathematics 2019-03-14 Ibrahim M. Nabiev

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

We consider an inverse spectral problem that consists in the recovery of the differential expression coefficients for higher-order operators with separated boundary conditions from the spectral data (eigenvalues and weight numbers). This…

Spectral Theory · Mathematics 2023-11-10 Natalia P. Bondarenko

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…

Analysis of PDEs · Mathematics 2025-07-15 Simone Creo , Maria Rosaria Lancia , Andrea Mola , Gianluca Mola , Silvia Romanelli