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The Sommerfeld half‐plane problem revisited, V: The bifurcated guide with mixed boundary conditions on the septum
Author(s) -
Heins Albert E.
Publication year - 1990
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/mma.1670120502
Subject(s) - mathematics , boundary value problem , neumann boundary condition , mathematical analysis , mixed boundary condition , dirichlet distribution , dirichlet problem , duct (anatomy) , robin boundary condition , dirichlet boundary condition , upper and lower bounds , medicine , pathology
We discuss the solution of the boundary value problem in a duct with a centered septum [9]. On the lower wall of the duct a Neumann condition is applied while on the upper wall a Dirichlet condition is applied. On the septum we apply a Dirichlet condition on the lower side and a Neumann condition on the upper one. This problem is formulated as a pair of integral equations of the Wiener–Hopf type for which we supply solutions for two modes of excitation as well as real and complex wave number. A critical examination is made of the construction, which reduces the problem to one in complex analysis. For real wave number, the physical parameters are provided in very simple forms.