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Generalized boundary and transition conditions and the question of uniqueness
Author(s) -
Senior Thomas B. A.
Publication year - 1992
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/92rs01426
Subject(s) - classification of discontinuities , uniqueness , directional derivative , mathematics , boundary value problem , boundary (topology) , surface (topology) , order (exchange) , third order , mathematical analysis , field (mathematics) , enhanced data rates for gsm evolution , boundary layer , geometry , pure mathematics , computer science , physics , mechanics , telecommunications , philosophy , theology , finance , economics
To better simulate the material properties of a surface, a method that is attracting attention is to include higher derivatives in the boundary specification of the field. In the case of a thin layer, the result is a generalized boundary or transition condition whose order is specified by the highest ( N th) derivative present. The conditions are logical extensions of the first order ones corresponding to the usual surface impedance or sheet conditions, but when applied to a surface with discontinuities, they do not produce a unique solution to the problem if N > 1. The standard edge conditions alone are no longer sufficient and additional constraints are necessary. It is shown how these can be obtained from a rather general derivation of the conditions, applicable for conditions through at least the third order.