TY - JOUR

T1 - The Maxwell system in waveguides with several cylindrical outlets to infinity and nonhomogeneous anisotropic filling

AU - Plamenevskiĭ, B. A.

AU - Poretskiĭ, A. S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A waveguide occupies a domain G in ℝ3 with several cylindrical outlets to infinity; the boundary ∂G is assumed to be smooth. The dielectric ε and magnetic μ permittivities are matrix-valued functions smooth and positive definite in G. At every cylindrical outlet, the matrices e and μ tend, at infinity, to limit matrices independent of the axial variable. The limit matrices can be arbitrary smooth and positive definite matrix-valued functions of the transverse coordinates in the corresponding cylinder. In such a waveguide, the stationary Maxwell system with perfectly conducting boundary conditions and a real spectral parameter is considered. In the presence of charges and currents, the corresponding boundary value problem with radiation conditions turns out to be well posed. A unitary scattering matrix is also defined. The Maxwell system is extended to an elliptic system. The results for the Maxwell system are derived from those obtained for the elliptic problem.

AB - A waveguide occupies a domain G in ℝ3 with several cylindrical outlets to infinity; the boundary ∂G is assumed to be smooth. The dielectric ε and magnetic μ permittivities are matrix-valued functions smooth and positive definite in G. At every cylindrical outlet, the matrices e and μ tend, at infinity, to limit matrices independent of the axial variable. The limit matrices can be arbitrary smooth and positive definite matrix-valued functions of the transverse coordinates in the corresponding cylinder. In such a waveguide, the stationary Maxwell system with perfectly conducting boundary conditions and a real spectral parameter is considered. In the presence of charges and currents, the corresponding boundary value problem with radiation conditions turns out to be well posed. A unitary scattering matrix is also defined. The Maxwell system is extended to an elliptic system. The results for the Maxwell system are derived from those obtained for the elliptic problem.

KW - Elliptic extension

KW - Radiation principle

KW - Scattering matrix

KW - scattering matrix

KW - elliptic extension

UR - http://www.scopus.com/inward/record.url?scp=85043530951&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=35544717

U2 - 10.1090/spmj/1494

DO - 10.1090/spmj/1494

M3 - Article

AN - SCOPUS:85043530951

VL - 29

SP - 289

EP - 314

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -