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A new numerical method to solve an inverse source problem for the radiative transfer equation involving the absorption and scattering terms, with incomplete data, is proposed. No restrictive assumption on those absorption and scattering…

Numerical Analysis · Mathematics 2019-04-02 Alexey V. Smirnov , Michael V. Klibanov , Loc H. Nguyen

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

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 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

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

This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…

Analysis of PDEs · Mathematics 2026-04-14 Qiling Gu , Wenlong Zhang , Zhidong Zhang

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…

Numerical Analysis · Mathematics 2022-12-20 Deyue Zhang , Yue Wu , Yukun Guo

We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes string. We offer three methods of recovering unknown parameters:…

Analysis of PDEs · Mathematics 2025-05-12 Alexander Mikhaylov , Victor Mikhaylov

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…

Numerical Analysis · Mathematics 2026-03-11 Fenglin Sun , Hongxia Guo

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…

Analysis of PDEs · Mathematics 2020-01-08 Xia Ji , Xiaodong Liu

Through coupled physics, we study an early-warning inverse source problem for the elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and…

Analysis of PDEs · Mathematics 2023-04-07 Lorenzo Baldassari , Maarten V. de Hoop , Elisa Francini , Sergio Vessella

In this paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Barcilon's three spectra with the Weyl-Yurko matrix. Moreover,…

Spectral Theory · Mathematics 2023-04-13 Aiwei Guan , Chuanfu Yang , Natalia P. Bondarenko

This work investigates an inverse problem of determining the radiative coefficient in a degenerate parabolic equation from the final overspecified data. Being different from other inverse coefficient problems in which the principle…

Optimization and Control · Mathematics 2013-10-01 Zui-Cha Deng , Liu Yang

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

Analysis of PDEs · Mathematics 2019-04-12 Daijun Jiang , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

The dynamical system under consideration is \begin{align*} & u_{tt}-u_{xx}+Vu=0,\qquad x>0,\,\,\,t>0;\\ & u|_{t=0}=u_t|_{t=0}=0,\,\,x\geqslant 0;\quad u|_{x=0}=f,\,\,t\geqslant 0, \end{align*} where $V=V(x)$ is a matrix-valued function…

Mathematical Physics · Physics 2020-06-26 Mikhail Belishev , Timur Khabibullin

This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…

Analysis of PDEs · Mathematics 2020-04-08 Elham Sohrabi

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh

We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results…

Analysis of PDEs · Mathematics 2024-07-09 Roman Novikov , Basant Lal Sharma

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…

Analysis of PDEs · Mathematics 2020-03-13 Guanghui Hu , Jingzhi Li

In this paper we explore the weak solution of a time-dependent inverse source problem and inverse initial problem for $q$-analogue of the heat equation. As an over-determination condition we have used integral type condition on…

Analysis of PDEs · Mathematics 2022-12-15 Erkinjon Karimov , Serikbol Shaimardan