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Related papers: On an inverse source problem for the Biot's equati…

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An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…

Analysis of PDEs · Mathematics 2016-09-14 Jaan Janno , Kairi Kasemets

In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of…

Numerical Analysis · Mathematics 2021-05-19 Bangti Jin , Yavar Kian , Zhi Zhou

In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and uniqueness of reconstruction. Our approach…

Spectral Theory · Mathematics 2012-05-22 Nataliya Pronska

A Gaussian elimination form of inverse iteration within the complex coordinate approach is shown to produce a simple uniform method of finding both real bound state energies and complex resonant state energies for several problems which…

Quantum Physics · Physics 2009-06-25 John P. Killingbeck , Alain Grosjean

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

Numerical Analysis · Mathematics 2022-11-23 Guang Lin , Zecheng Zhang , Zhidong Zhang

In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies…

Analysis of PDEs · Mathematics 2025-06-17 Suliang Si

A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of…

Numerical Analysis · Mathematics 2009-12-06 G. Zangerl , O. Scherzer , M. Haltmeier

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

Analysis of PDEs · Mathematics 2022-07-15 Jaan Janno , Yavar Kian

We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…

Mathematical Physics · Physics 2016-07-18 Liliana Borcea , Ilker Kocyigit

An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…

Computational Physics · Physics 2011-01-06 Clinton DeW. Van Siclen

We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…

Analysis of PDEs · Mathematics 2019-02-20 Loc Hoang Nguyen

The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…

Analysis of PDEs · Mathematics 2021-09-07 Barbara Kaltenbacher

A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure. The discretization under focus is the…

Numerical Analysis · Mathematics 2020-11-19 F. Bertrand , G. Starke

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…

Analysis of PDEs · Mathematics 2021-11-08 Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…

Analysis of PDEs · Mathematics 2017-08-03 Guillaume Bal , Kristoffer Hoffmann , Kim Knudsen

This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…

Numerical Analysis · Mathematics 2023-09-25 Tran H. Lan , Dinh-Liem Nguyen

We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency. We prove the resolution of the reconstruction…

Numerical Analysis · Mathematics 2019-07-24 Zhiming Chen , Shiqi Zhou

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…

Optimization and Control · Mathematics 2024-12-17 Ugur G. Abdulla , Saleheh Seif