An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number
From MaRDI portal
Publication:3097927
DOI10.1088/0266-5611/27/10/105001zbMath1231.35299OpenAlexW2037465252MaRDI QIDQ3097927
Abdellatif El Badia, Takaaki Nara
Publication date: 10 November 2011
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0266-5611/27/10/105001
Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items (57)
A harmonic function method for EEG source reconstruction ⋮ Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data ⋮ Reconstruction of the electric field of the Helmholtz equation in three dimensions ⋮ Inverse Random Source Scattering Problems in Several Dimensions ⋮ Recovering multiple small inclusions in a three-dimensional domain using a single measurement ⋮ Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems ⋮ Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem ⋮ Retrieval of acoustic sources from multi-frequency phaseless data ⋮ Identification of points sources via time fractional diffusion equation ⋮ Recovering simultaneously a potential and a point source from Cauchy data ⋮ Reconstruction of extended sources with small supports in the elliptic equation \(\Delta u+\mu u=F\) from a single Cauchy data ⋮ The method of fundamental solutions for pointwise source reconstruction ⋮ Shape optimization method for an inverse geometric source problem and stability at critical shape ⋮ Hölder stability estimates for some inverse pointwise source problems ⋮ Reconstruction of pointwise sources in a time-fractional diffusion equation ⋮ Inverse Random Source Scattering for Elastic Waves ⋮ Reconstruction algorithms of an inverse source problem for the Helmholtz equation ⋮ Mathematical design of a novel input/instruction device using a moving acoustic emitter ⋮ Reconstruction of Multiscale Elastic Sources from Multifrequency Sparse Far Field Patterns ⋮ On the recovery of internal source for an elliptic system by neural network approximation ⋮ Stability for the electromagnetic inverse source problem in inhomogeneous media ⋮ A data-driven model reduction method for parabolic inverse source problems and its convergence analysis ⋮ On reconstruction of small sources from Cauchy data at a fixed frequency ⋮ Phaseless inverse source scattering problem: phase retrieval, uniqueness and direct sampling methods ⋮ Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data ⋮ Mathematical analysis and numerical methods for inverse scattering problems ⋮ Inverse random source scattering for the Helmholtz equation in inhomogeneous media ⋮ A Tikhonov-type regularization method for identifying the unknown source in the modified Helmholtz equation ⋮ Fourier method for recovering acoustic sources from multi-frequency far-field data ⋮ Stability on the one-dimensional inverse source scattering problem in a two-layered medium ⋮ Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves ⋮ Lipschitz stability for an inverse source scattering problem at a fixed frequency * ⋮ Stability for the Acoustic Inverse Source Problem in Inhomogeneous Media ⋮ Logarithmic stability estimates for an inverse source problem from interior measurements ⋮ Inverse Source Problems for Maxwell's Equations and the Windowed Fourier Transform ⋮ Solving the multi-frequency electromagnetic inverse source problem by the Fourier method ⋮ Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation ⋮ Radiating and non-radiating sources in elasticity ⋮ On inverse problems for characteristic sources in Helmholtz equations ⋮ Locating Multiple Multipolar Acoustic Sources Using the Direct Sampling Method ⋮ Source Reconstruction with Multifrequency Sparse Scattered Fields ⋮ Stability for the inverse source problems in elastic and electromagnetic waves ⋮ Identifying multipolar acoustic sources by the direct sampling method ⋮ Stability estimates for point sources identification problem using reciprocity gap concept via the Helmholtz equation ⋮ Inverse random source problems for time-harmonic acoustic and elastic waves ⋮ Imaging point sources in heterogeneous environments ⋮ Lipschitz stability estimates for an inverse source problem in an elliptic equation from interior measurements ⋮ Identification and stability of small-sized dislocations using a direct algorithm ⋮ Reconstruction of multipolar point sources with multi-frequency sparse far field data ⋮ Inverse Elastic Scattering for a Random Source ⋮ An energetic boundary functional method for solving the inverse source problems of 2D nonlinear elliptic equations ⋮ Improved integral formulae for supersonic reconstruction of the acoustic field ⋮ Recovering point sources for the inhomogeneous Helmholtz equation * ⋮ An efficient and robust algorithm for source reconstruction in the Helmholtz equation ⋮ Recovery of dipolar sources and stability estimates ⋮ A non-iterative reconstruction method for bioluminescence tomography ⋮ Direct algorithm for multipolar sources reconstruction
This page was built for publication: An inverse source problem for Helmholtz's equation from the Cauchy data with a single wave number
