On the characterization of the Fréchet derivative with respect to a Lipschitz domain of the acoustic scattered field

DOI10.1006/jmaa.1999.6536zbMath0937.35175OpenAlexW2084078381MaRDI QIDQ1307267

Rabia Djellouli, Charbel Farhat

Publication date: 1 December 1999

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6536

zbMATH Keywords

Fréchet differentiabilityscatteringacousticsinverse scatteringLipschitz domaindomain derivative

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Diffraction, scattering (78A45) Hydro- and aero-acoustics (76Q05) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

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Variational approach to shape derivatives for elasto-acoustic coupled scattering fields and an application with random interfaces ⋮ A least-squares FEM for the direct and inverse rectangular cavity scattering problem ⋮ Bayesian method for shape reconstruction in the inverse interior scattering problem ⋮ Fréchet differentiability of the elasto-acoustic scattered field with respect to Lipschitz domains ⋮ Mathematical Determination of the Fréchet Derivative with Respect to the Domain for a Fluid-Structure Scattering Problem: Case of Polygonal-Shaped Domains ⋮ Inverse Obstacle Scattering in an Unbounded Structure ⋮ Inverse obstacle scattering for Maxwell’s equations in an unbounded structure

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• Newton-Kantorovich method applied to two-dimensional inverse scattering for an exterior Helmholtz problem
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• The domain derivative and two applications in inverse scattering theory
• Frechet differentiability of boundary integral operators in inverse acoustic scattering
• Frechet derivatives in inverse obstacle scattering
• Fréchet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain
• Inverse acoustic and electromagnetic scattering theory

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