An inverse scattering problem with generalized oblique derivative boundary condition

2016 ◽  
Vol 108 ◽  
pp. 226-241 ◽  
Author(s):  
Haibing Wang ◽  
Jijun Liu
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem

Far field patterns and inverse scattering problems for imperfectly conducting obstacles

1989 ◽  
Vol 106 (3) ◽  
pp. 553-569 ◽  
Author(s):  
T. S. Angell ◽  
David Colton ◽  
Rainer Kress
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Far Field ◽  
Scattering Problems ◽  
Impedance Boundary ◽  
Field Patterns

AbstractWe first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.

Inverse scattering problem for the nonstationary Dirac equation on the half-plane

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Mansur I. Ismailov
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Inverse Scattering ◽  
Half Plane ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dirac System ◽  
Scattering Operator ◽  
Uniqueness Criterion

AbstractIn this paper, the inverse scattering problem for the nonstationary Dirac system on the half-plane is considered. The uniqueness criterion for the inverse scattering problem in terms of boundary condition is described and the restoration of the potential from the scattering operator is proved.

scholarly journals The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yao Mao ◽  
Yongguang Chen ◽  
Jun Guo
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Surface Impedance ◽  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Mathematical Basis ◽  
Impedance Boundary

We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.

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