On the boundary value problem associated with a general twisted tube with a uniform nonrotating section

Murray, J. C.

doi:10.1090/qam/636239

Author: J. C. Murray
Journal: Quart. Appl. Math. 39 (1981), 341-349
MSC: Primary 31B20; Secondary 73C50
DOI: https://doi.org/10.1090/qam/636239
MathSciNet review: 636239
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Abstract: An orthogonal curvilinear coordinate system is used to formulate the Dirichlet problem of potential theory associated with the interior of a general twisted tube with a uniform non-rotating section. Two solution schemes are presented for a class of finite and infinite tube geometries. The boundary-value problems associated with a tube of uniform circular section are discussed as an example.

J. C. Murray, Curvilinear coordinate systems associated with a class of boundary value problems, J. Inst. Math. Appl. 25 (1980), no. 4, 397–411. MR 578086
Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774