Plane Wave Solutions to the Equations of Electrodynamics in an Anisotropic Medium

被引:0
作者
V. G. Romanov
机构
[1] Sobolev Institute of Mathematics,
来源
Siberian Mathematical Journal | 2019年 / 60卷
关键词
Maxwell’s equations; anisotropy; plane wave; structure of a solution;
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摘要
Under examination is the system of equations of electrodynamics for a nonconducting nonmagnetic medium with the simplest anisotropy of permittivity. We assume that permittivity is characterized by the diagonal matrix ϵ = diag(ε1, ε1, ε2), with the functions ε1 and ε2 equal to positive constants beyond a bounded convex domain Ω ⊂ ℝ3. Two modes of traveling plane waves exist in a homogeneous anisotropic medium. The structure is studied of the solutions related to the traveling plane waves incident from infinity on an inhomogeneity located in Ω.
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页码:661 / 672
页数:11
相关论文
共 21 条
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Romanov V G(1986)Structure of a fundamental solution to the Cauchy problem for Maxwell’s equations Differ. Uravn. 22 1577-1587
[2]  
Romanov V G(2017)The problem of recovering the permittivity coefficient from the modulus of the scattered electromagnetic field Sib. Math. J. 58 711-717
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Romanov V G(2017)Problem of determining the permittivity in the stationary system of Maxwell equations Dokl. Math. 95 230-234
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Klibanov M V(2015)The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation J. Inverse Ill-Posed Probl. 23 415-428
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Romanov V G(2015)Explicit solution of 3-D phaseless inverse scattering problems for the Schrödinger equation: the plane wave case Euras. J. Math. Comput. Appl. 3 48-63
[6]  
Klibanov M V(2015)Explicit formula for the solution of the phaseless inverse scattering problem of imaging of nanostructures J. Inverse Ill-Posed Probl. 23 187-193
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Romanov V G(2015)Some geometric aspects in inverse problems Eurasian J. Math. Comput. Appl. 3 68-84
[8]  
Klibanov M V(2016)Reconstruction procedures for two inverse scattering problem without the phase information SIAM J. Appl. Math. 76 178-196
[9]  
Romanov V G(2016)Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation Inverse Problems 32 015005-688
[10]  
Romanov V G(2017)Uniqueness of a 3-D coefficient inverse scattering problem without the phase information Inverse Problems 33 095007-91