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Related papers: Point sources identification problems with pointwi…

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Starting with far field data of time-harmonic acoustic or electromagnetic waves radiated by a collection of compactly supported sources in two-dimensional free space, we develop criteria and algorithms for the recovery of the far field…

Analysis of PDEs · Mathematics 2016-07-20 Roland Griesmaier , John Sylvester

In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…

Analysis of PDEs · Mathematics 2016-01-22 M. S. Salakhitdinov , E. T. Karimov

We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…

Numerical Analysis · Mathematics 2023-11-21 Lingyun Qiu , Zhongjing Wang , Hui Yu , Shenwen Yu

In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…

Analysis of PDEs · Mathematics 2020-12-30 X. Huang , O. Yu. Imanuvilov , M. Yamamoto

We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…

Analysis of PDEs · Mathematics 2025-03-18 Matti Lassas

This work includes a number of novel contributions for the multiple-source adaptation problem. We present new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new…

Machine Learning · Computer Science 2018-05-23 Judy Hoffman , Mehryar Mohri , Ningshan Zhang

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…

Numerical Analysis · Mathematics 2023-07-06 Yan Chang , Yukun Guo , Tao Yin , Yue Zhao

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…

Analysis of PDEs · Mathematics 2021-07-20 Isaac Harris , Dinh-Liem Nguyen , Thi-Phong Nguyen

This work presents a mathematical model to enable rapid prediction of airborne contaminant transport based on scarce sensor measurements. The method is designed for applications in critical infrastructure protection (CIP), such as…

Numerical Analysis · Mathematics 2026-02-05 Marco Mattuschka , Daniel Walter , Max von Danwitz , Alexander Popp

The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of…

Analysis of PDEs · Mathematics 2025-06-16 R. R. Ashurov , O. T. Mukhiddinova

Determining the number of change-points is a first-step and fundamental task in change-point detection problems, as it lays the groundwork for subsequent change-point position estimation. While the existing literature offers various methods…

Methodology · Statistics 2026-03-31 Ao Sun , Jingyuan Liu

Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…

Numerical Analysis · Mathematics 2025-06-16 Carola-Bibiane Schönlieb , Zakhar Shumaylov

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…

Analysis of PDEs · Mathematics 2025-07-15 Simone Creo , Maria Rosaria Lancia , Andrea Mola , Gianluca Mola , Silvia Romanelli

This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A…

Numerical Analysis · Mathematics 2018-11-30 Zhicheng Hu , Keiwei Liang

We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…

Analysis of PDEs · Mathematics 2025-09-18 Nana Meng

We report the experimental super-resolution of pairs of point-like fluorescent sources using a modified image inversion interferometer microscope. The technique is inspired by recent developments in the application of quantum parameter…

The aim of this paper is to solve an important inverse source problem which arises from the well-known inverse scattering problem. We propose to truncate the Fourier series of the solution to the governing equation with respect to a special…

Numerical Analysis · Mathematics 2022-10-18 Loc H. Nguyen , Huong T. Vu

This paper is devoted to the study of source reconstruction algorithms for coupled systems of heat equations, with either constant or spatially dependent coupling terms, where internal measurements are available from a reduced number of…

Optimization and Control · Mathematics 2026-02-05 Cristhian Montoya , Ignacio Brevis , David Bolivar

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid

We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…

Numerical Analysis · Mathematics 2013-09-10 Jiang Daijun , Feng Hui , Zou Jun