Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction

DOI10.1063/1.530279zbMath0785.35110OpenAlexW1980468417MaRDI QIDQ4276790

Sailing He, Staffan Ström, Vladimir G. Romanov, Sergey I. Kabanikhin

Publication date: 27 April 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530279

zbMATH Keywords

convergenceexistenceuniquenessGreen's functionfundamental solutionwave splittingstability estimateslocal correctnessone-dimensional electromagnetic inverse problem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Inverse problems for PDEs (35R30) Diffraction, scattering (78A45) Waves and radiation in optics and electromagnetic theory (78A40)

Related Items (2)

Analysis of the Green’s function approach to one-dimensional inverse problems. II. Simultaneous reconstruction of two parameters ⋮ Inverse problem of electrodynamics for anisotropic medium: linear approximation

Cites Work

• Obtaining scattering kernels using invariant imbedding
• A Green's function approach to the determination of internal fields
• Wave splitting in the time domain for a radially symmetric geometry
• Invariant imbedding for the wave equation in three dimensions and the applications to the direct and inverse problems
• Direct and inverse scattering in the time domain for a dissipative wave equation. I. Scattering operators
• Direct and inverse scattering in the time domain for a dissipative wave equation. II. Simultaneous reconstruction of dissipation and phase velocity profiles
• A Wave Splitting Approach to Time Dependent Inverse Scattering for the Stratified Cylinder
• Inverse problem for the dissipative wave equation in a stratified half-space and linearization of the imbedding equations
• Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile
• Invariant imbedding and wave splitting in R ³  : II. The Green function approach to inverse scattering
• Direct and inverse scattering in the time domain for a dissipative wave equation. Part IV: Use of phase velocity mismatches to simplify inversions
• Direct and inverse scattering in the time domain for a dissipative wave equation. III. Scattering operators in the presence of a phase velocity mismatch

This page was built for publication: Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction