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The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…

Analysis of PDEs · Mathematics 2018-05-16 Oleg Yaremko , Lidia Simutina

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

Analysis of PDEs · Mathematics 2023-05-17 Bastian Harrach

The inverse fixed angle problem for operator $\Delta^2 u + V(x,|u|) u$ is considered in dimensions $n=2,3$. We prove that the difference between an inverse fixed angle Born approximation and the function $V(\cdot,1)$ is smoother than the…

Analysis of PDEs · Mathematics 2022-09-29 Jaakko Kultima

We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].

Analysis of PDEs · Mathematics 2011-05-17 Oleg Imanuvilov , Masahiro Yamamoto

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

Analysis of PDEs · Mathematics 2023-04-25 Xiaomeng Zhao , Ganghua Yuan

Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…

Numerical Analysis · Mathematics 2024-12-16 Bosu Choi , Jihun Han , Yoonsang Lee

We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Bruce Alastair Watson

We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…

Numerical Analysis · Mathematics 2025-03-25 Roman Chapko , Leonidas Mindrinos

The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be…

Classical Analysis and ODEs · Mathematics 2023-10-12 Vladimir Mikhailets , Olena Atlasiuk

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

This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…

Analysis of PDEs · Mathematics 2023-03-14 Sean Holman , Vasiliki Torega

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha

We consider the Schr\"{o}dinger operator on a finite interval with an $L^1$-potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or…

Spectral Theory · Mathematics 2023-10-25 Burak Hatinoğlu

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic…

Analysis of PDEs · Mathematics 2025-09-16 Cătălin I. Cârstea , Ali Feizmohammadi

In this paper, we consider a nonlocal boundary-value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional derivative in a rectangular domain. The main target of this work is to analyze the uniqueness and the…

Analysis of PDEs · Mathematics 2021-06-25 Erkinjon Karimov , Bakhodirjon Toshtemirov

In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…

Spectral Theory · Mathematics 2023-03-29 Natalia P. Bondarenko

The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…

Numerical Analysis · Mathematics 2026-05-05 Tielei Zhu , Zhihao Ge , Bangmin Wu

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

Spectral Theory · Mathematics 2021-07-27 Natalia P. Bondarenko

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Analysis of PDEs · Mathematics 2016-09-21 Kais Ammari , Mourad Choulli , Faouzi Triki