An inverse acoustic scattering problem for an obstacle with an impedance boundary condition

DOI10.1016/0022-247X(85)90052-6zbMath0571.35108MaRDI QIDQ1061948

Robert T. Smith

Publication date: 1985

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

zbMATH Keywords

inverse problemconformal mappingFourier serieswave diffractionintegral equation methodsimpedance conditionwell-posedbounded obstaclefar field patternsFredholm equation of the first kindlow-frequency patterns

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Diffraction, scattering (78A45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (10)

Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium ⋮ The determination of the surface impedance of an obstacle ⋮ An inverse scattering problem from an impedance obstacle ⋮ On stability for a translated obstacle with impedance boundary condition ⋮ Reconstruction and uniqueness of an inverse scattering problem with impedance boundary ⋮ Inverse scattering problem from an impedance obstacle via two-steps method ⋮ Recovery of multiple obstacles by probe method ⋮ Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization ⋮ High Precision Identification of an Object: Optimality-Conditions-Based Concept of Imaging ⋮ Numerical investigations with extended isogeometric boundary element analysis (XIBEM) for direct and inverse Helmholtz acoustic problems

Cites Work

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• The Determination of the Surface Impedance of an Obstacle from Measurements of the Far Field Pattern
• Stable methods for determining the surface impedance of an obstacle from low frequency far field data
• The Inverse Problem of Acoustic Scattering
• On Tikhonov's Method for Ill-Posed Problems
• The inverse electromagnetic scattering problem for a perfectly conducting cylinder
• Inverse scattering for an exterior Dirichlet problem
• Applications of functional analysis and operator theory

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