Inverse Source Problems in an Inhomogeneous Medium with a Single Far-Field Pattern

DOI10.1137/20M1325289zbMath1467.35348arXiv1907.08390OpenAlexW3094050932MaRDI QIDQ5130520

Jingzhi Li, Guanghui Hu

Publication date: 4 November 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.08390

zbMATH Keywords

Helmholtz equationsingle measurementconvex-polygonal source termscorner scattering theorytime-harmonic inverse source problems

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Polyhedra and polytopes; regular figures, division of spaces (51M20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Uniqueness in determining rectangular grating profiles with a single incoming wave (Part I): TE polarization case ⋮ Uniqueness in determining rectangular grating profiles with a single incoming wave (part II): TM polarization case ⋮ Direct sampling method to inverse wave-number-dependent source problems: determination of the support of a stationary source ⋮ Stability of a one-dimensional inverse source scattering problem in a multi-layered medium ⋮ Uniqueness and numerical scheme for spherical shell-structured sources from the far field patterns with at most two frequencies ⋮ Factorization method with one plane wave: from model-driven and data-driven perspectives ⋮ Determination of piecewise homogeneous sources for elastic and electromagnetic waves ⋮ Inverse Time-Harmonic Electromagnetic Scattering from Coated Polyhedral Scatterers With a Single Far-Field Pattern ⋮ Uniqueness for time-dependent inverse problems with single dynamical data ⋮ Piecewise-analytic interfaces with weakly singular points of arbitrary order always scatter

Cites Work

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• A qualitative approach to inverse scattering theory
• A multi-frequency inverse source problem
• Corners always scatter
• Elliptic problems in domains with piecewise smooth boundaries
• Inverse acoustic and electromagnetic scattering theory.
• On the uniqueness in the inverse conductivity problem
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• Elliptic partial differential equations of second order
• Strictly convex corners scatter
• Acoustic scattering from corners, edges and circular cones
• Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type
• Uniqueness to some inverse source problems for the wave equation in unbounded domains
• On imaging obstacles inside inhomogeneous media
• An inverse transmission scattering problem and the enclosure method
• Inverse Modeling
• The factorization method for inverse acoustic scattering in a layered medium
• Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements
• Shape Identification in Inverse Medium Scattering Problems with a Single Far-Field Pattern
• Acoustic source identification using multiple frequency information
• Reconstruction of a source domain from the Cauchy data
• A  range test  for determining scatterers with unknown physical properties
• The scattering support
• On reconstruction in the inverse conductivity problem with one measurement
• Nonradiating Sources and Transmission Eigenfunctions Vanish at Corners and Edges
• Interface with weakly singular points always scatter
• Extended sampling method in inverse scattering
• Unique determination of a penetrable scatterer of rectangular type for inverse Maxwell equations by a single incoming wave
• Corners and edges always scatter
• Uniqueness and factorization method for inverse elastic scattering with a single incoming wave
• Notions of support for far fields

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