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Implicit operator differential equations and applications to electrodynamics
Author(s) -
Rutkas A.,
Vlasenko L.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(20000110)23:1<1::aid-mma100>3.0.co;2-5
Subject(s) - mathematics , operator (biology) , uniqueness , boundary value problem , maxwell's equations , mathematical analysis , differential equation , differential operator , biochemistry , chemistry , repressor , transcription factor , gene
A cylindrical waveguide with layered dispersive medium is considered. An implicit operator differential equation of second order is obtained by separating variables in the corresponding boundary‐value problem for Maxwell's equations. Existence and uniqueness theorems are proved and explicit formulae for solutions are given. The spectral theory of operators and operator sheaves are used. Copyright © 2000 John Wiley & Sons, Ltd.