Inverse source problem with a posteriori boundary measurement for fractional diffusion equations
Sign Up to like & getrecommendations! Published in 2022 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.9432
Abstract: 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 of… read more here.
Keywords: fractional diffusion; time; diffusion equations; inverse source ... See more keywords
Simulation of 2D and 3D inverse source problems of nonlinear time-fractional wave equation by the meshless homogenization function method
Sign Up to like & getrecommendations! Published in 2021 at "Engineering with Computers"
DOI: 10.1007/s00366-021-01489-2
Abstract: In this paper, homogenization functions are first proposed to address two-dimensional (2D) and three-dimensional (3D) inverse source problems of nonlinear time-fractional wave equation (ISPs-NTFWE). Homogenization functions for 2D and 3D problems can be derived based… read more here.
Keywords: problems nonlinear; method; inverse source; source problems ... See more keywords
Inverse Source and Coefficient Problems for Elliptic and Parabolic Equations in Hölder and Sobolev Spaces
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-019-04184-2
Abstract: We review some results obtained by the authors during the last 15 years. In particular, we present the existence and uniqueness theorems for linear and nonlinear inverse problems of reconstructing unknown coefficients in elliptic and… read more here.
Keywords: elliptic parabolic; source coefficient; problems elliptic; inverse source ... See more keywords
Inverse source problems in transport equations with external forces
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DOI: 10.1016/j.jde.2021.09.011
Abstract: This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,… read more here.
Keywords: equations external; source; inverse source; problems transport ... See more keywords
Increasing stability for the inverse source problem in elastic waves with attenuation
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DOI: 10.1017/s0956792523000116
Abstract: This paper is concerned with the increasing stability of the inverse source problem for the elastic wave equation with attenuation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the… read more here.
Keywords: stability inverse; inverse source; source problem; source ... See more keywords
An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations
Sign Up to like & getrecommendations! Published in 2017 at "Inverse Problems in Science and Engineering"
DOI: 10.1080/17415977.2016.1201663
Abstract: This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a… read more here.
Keywords: fluid; inverse source; problem; pore fluid ... See more keywords
Inverse source problems for a space–time fractional differential equation
Sign Up to like & getrecommendations! Published in 2019 at "Inverse Problems in Science and Engineering"
DOI: 10.1080/17415977.2019.1597079
Abstract: ABSTRACT We considered two inverse source problems for a space–time fractional differential equation. Firstly recovery of a space dependent source term is studied, secondly determination of a time dependent source term is considered. A bi-orthogonal… read more here.
Keywords: problems space; source; time; inverse source ... See more keywords
A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium
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DOI: 10.1088/1361-6420/ab4d98
Abstract: We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering coefficients are… read more here.
Keywords: source problem; inverse; source; scattering medium ... See more keywords
Inverse Source Problem for a Host Medium Having Pointlike Inhomogeneities
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Geoscience and Remote Sensing"
DOI: 10.1109/tgrs.2018.2809913
Abstract: The reconstruction of a source embedded within a multipath environment, which is created by inserting a grid of point scatterers in the scene, is addressed. In particular, the source Fourier spectrum is assumed known so… read more here.
Keywords: resolution; source; inverse source; resolution improvement ... See more keywords
A Sampling Framework for Solving Physics-Driven Inverse Source Problems
Sign Up to like & getrecommendations! Published in 2017 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2017.2742983
Abstract: Partial differential equations are central to describing many physical phenomena. In many applications, these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain results in sampling… read more here.
Keywords: inverse source; source problems; framework solving; physics ... See more keywords