English
Related papers

Related papers: Inverse boundary value problems for polyharmonic o…

200 papers

We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…

Spectral Theory · Mathematics 2014-10-15 D. V. Puyda

This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…

Numerical Analysis · Mathematics 2026-03-10 Long-Ling Du , Zejun Sun , Li-Li Wang , Guang-Hui Zheng

In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.

Spectral Theory · Mathematics 2007-05-23 Rakib Feyruz Efendiev

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…

Spectral Theory · Mathematics 2018-02-08 Natalia Bondarenko , Vjacheslav Yurko

In this paper, we revisit McLaughlin's inverse problem, which consists in the recovery of the fourth-order differential operator from the eigenvalues and two sequences of weight numbers. We for the first time prove the uniqueness for…

Spectral Theory · Mathematics 2023-12-27 Natalia P. Bondarenko

We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We…

Analysis of PDEs · Mathematics 2023-07-06 Kui Ren , Nathan Soedjak

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and…

Classical Analysis and ODEs · Mathematics 2016-10-31 Khanlar R. Mamedov , Done Karahan

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…

Spectral Theory · Mathematics 2023-10-25 Burak Hatinoğlu

In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…

Numerical Analysis · Mathematics 2020-04-02 Dang Quang A , Nguyen Quoc Hung , Vu Vinh Quang

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

Analysis of PDEs · Mathematics 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional…

Analysis of PDEs · Mathematics 2017-08-01 Ariel Barton

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…

Analysis of PDEs · Mathematics 2021-11-01 G. Yu. Mehdiyeva , Y. T. Mehraliyev , E. I. Azizbayov

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

We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , O. Y. Imanuvilov , Masahiro Yamamoto

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi