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In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-\Delta_g)^s)u := \sum_{i=1}^M \alpha_i(-\Delta_{g_i})^{s_i}u\] for $s=(s_1,\dots,s_M)$,…

Analysis of PDEs · Mathematics 2025-05-14 Ching-Lung Lin , Hongyu Liu , Catharine W. K. Lo

We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…

Analysis of PDEs · Mathematics 2021-01-15 Gunther Uhlmann , Jian Zhai

We study inverse boundary problems for first order perturbations of the biharmonic operator on a conformally transversally anisotropic Riemannian manifold of dimension $n \ge 3$. We show that a continuous first order perturbation can be…

Analysis of PDEs · Mathematics 2020-12-29 Lili Yan

Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.

Spectral Theory · Mathematics 2017-02-06 Vjacheslav Yurko

We study inverse boundary problems for third-order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$, where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we demonstrate…

Analysis of PDEs · Mathematics 2023-12-14 Sombuddha Bhattacharyya , Katya Krupchyk , Suman Kumar Sahoo , Gunther Uhlmann

In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…

Spectral Theory · Mathematics 2024-02-29 Ai-Wei Guan , Chuan-Fu Yang , Natalia P. Bondarenko

In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…

Analysis of PDEs · Mathematics 2022-11-08 Xiaomeng Zhao , Ganghua Yuan

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

Numerical Analysis · Mathematics 2020-12-25 Leon Bungert , Martin Burger , Yury Korolev , Carola-Bibiane Schoenlieb

This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…

Classical Analysis and ODEs · Mathematics 2016-10-25 Faouzi Haddouchi , Slimane Benaicha

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…

Classical Analysis and ODEs · Mathematics 2007-05-23 Leszek Gasinski , Nikolaos S. Papageorgiou

This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…

Analysis of PDEs · Mathematics 2021-09-21 Sombuddha Bhattacharyya , Tuhin Ghosh

First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral…

Spectral Theory · Mathematics 2017-05-17 Vjacheslav Yurko

An inverse problem for a nonlinear biharmonic operator is under consideration in the spirit of Isakov (1993) and Johansson-Nurminen-Salo (2023). We prove that a general nonlinear term of the $Q= Q(x,u, \nabla u, \Delta u)$ associated to a…

Analysis of PDEs · Mathematics 2025-04-10 Janne Nurminen , Suman Kumar Sahoo

We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…

Spectral Theory · Mathematics 2020-10-28 S. A. Buterin , M. A. Malyugina , C. -T. Shieh

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

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Analysis of PDEs · Mathematics 2025-11-27 Xiaoxu Xu , Guanghui Hu

We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…

Analysis of PDEs · Mathematics 2017-02-14 Alexey Agaltsov

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…

Classical Analysis and ODEs · Mathematics 2022-08-04 A. Sinan Ozkan , İbrahim Adalar

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