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In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

Spectral Theory · Mathematics 2023-05-31 Feng Wang , Chuan-Fu Yang

This article deals with the multidimensional Borg-Levinson theorem for perturbed bi-harmonic operator. More precisely, in a bounded smooth domain of $\R^n$, with $n \geq 2$, we prove the stability of the first and zero order coefficients of…

Analysis of PDEs · Mathematics 2023-04-26 Nesrine Aroua , Mourad Bellassoued

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…

Classical Analysis and ODEs · Mathematics 2018-10-12 F. Alberto Grünbaum , Inés Pacharoni , Ignacio N. Zurrián

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…

Analysis of PDEs · Mathematics 2024-05-01 Boya Liu

Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…

Analysis of PDEs · Mathematics 2016-09-16 Fatma Al-Musalhi , Nasser Al-Salti , Sebti Kerbal

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

For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.

Spectral Theory · Mathematics 2020-07-20 Oles Dobosevych , Rostyslav Hryniv

In this work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

Analysis of PDEs · Mathematics 2021-04-27 Ibtissem Ben Aïcha , Guanghui Hu , Manmohan Vashisth , Jun Zou

This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…

Analysis of PDEs · Mathematics 2018-08-13 Zhiyuan Li , Kenichi Fujishiro , Gongsheng Li

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

Analysis of PDEs · Mathematics 2023-01-20 Bochao Chen , Yixian Gao , Shuguan Ji , Yang Liu

In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…

Analysis of PDEs · Mathematics 2023-05-02 Ravshan Ashurov , Yusuf Fayziev , Muattar Khudoykulova

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

Analysis of PDEs · Mathematics 2013-11-12 Yang Yang

We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…

Analysis of PDEs · Mathematics 2017-07-18 Gregory Eskin

We show that a complete Riemannian manifold, as well as time independent smooth lower order terms appearing in a first order symmetric perturbation of a Riemannian wave operator can be uniquely recovered, up to the natural obstructions,…

Analysis of PDEs · Mathematics 2025-05-01 Teemu Saksala , Andrew Shedlock

In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…

Analysis of PDEs · Mathematics 2024-10-02 Ru-Yu Lai , Hanming Zhou

This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forward problem is examined, and its unique solvability is…

Analysis of PDEs · Mathematics 2025-11-10 Ravshan Ashurov , Elbek Husanov

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…

Analysis of PDEs · Mathematics 2023-02-07 Li Li

The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…

Classical Analysis and ODEs · Mathematics 2008-04-15 R. F. Efendiev

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