Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Lakshtanov, Evgeny

doi:10.1088/1751-8113/43/12/125204

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…These general results are applied to a scattering problem for an obstacle coating by a springy layer. Some other results related to the topics discussed below can be found in [3,10].…”

Section: Introductionmentioning

confidence: 93%

Resonance regimes of scattering by small bodies with impedance boundary conditions

Lakshtanov¹,

Vainberg²

2010

J. Phys. A: Math. Theor.

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The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumannto-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when k = 0 is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position.Mathematics subject classifications: 35P25, 35Qxx,78A45

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“…These general results are applied to a scattering problem for an obstacle coating by a springy layer. Some other results related to the topics discussed below can be found in [3,10].…”

Section: Introductionmentioning

confidence: 93%

Resonance regimes of scattering by small bodies with impedance boundary conditions

Lakshtanov¹,

Vainberg²

2010

J. Phys. A: Math. Theor.

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High Frequency Scattering by a Classically Invisible Body

Lakshtanov¹,

Sleeman²,

Vainberg³

2012

SIAM J. Appl. Math.

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We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The quasiclassical approximation is obtained and justified in the case of impedance boundary conditions with a non zero absorbing part. It is shown that the total momentum transmitted to the obstacle vanishes when the frequency k goes to infinity, and that the total cross section oscillates at high frequencies. When the impedance λ 0 is real (i. e., there is no absorption), it is shown that there exists a sequence of frequencies k n such that the averages in the impedance of the total cross section over shrinking intervals around λ 0 go to zero as k n → ∞.

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Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Cited by 2 publications

References 17 publications

Resonance regimes of scattering by small bodies with impedance boundary conditions

Resonance regimes of scattering by small bodies with impedance boundary conditions

High Frequency Scattering by a Classically Invisible Body

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