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Scattering on a Compact Domain with Few Semi‐Infinite Wires Attached: Resonance Case
Author(s) -
Mikhailova A.,
Pavlov B.,
Popov I.,
Rudakova T.,
Yafyasov A.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200202)235:1<101::aid-mana101>3.0.co;2-v
Subject(s) - eigenfunction , transmission coefficient , mathematical analysis , mathematics , resonance (particle physics) , domain (mathematical analysis) , scattering , boundary (topology) , laplace operator , boundary value problem , neumann boundary condition , transmission (telecommunications) , semi infinite , physics , optics , quantum mechanics , eigenvalues and eigenvectors , telecommunications , computer science
Abstract A Scattering problem is studied for Neumann Laplacian with a continuous potential on a domain with a smooth boundary and few semi‐infinite wires attached to it at the points of contact on the boundary. In resonance case when the frequency of the incoming waves in the wires coincides with some resonance frequency of the domain the approximate formula for the transmission coefficient from one wire to another is derived: in the case of weak interaction between the domain and the wires the transmission coefficient is proportional to the product of values of the corresponding resonance eigenfunction of inner problem at the corresponding points of contact.