A generalization of Milne-Thomson theorem for the case of annulus
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 4, pp. 35-50
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A closed analytical solution to the problem on 2-D seepage flow with a given main part, $f(z)$, of a desired complex potential in an infinite heterogeneous three-component porous medium is presented. The medium is composed of an isotropic annulus and two other dissimilar components adding annulus up to the whole plane. New solutions are derived for the cases of arbitrary distribution of singularities of a given main part $f(z)$ including for the cases of singularities at the interface. Besides, the cases involving complex coefficients in the boundary conditions are considered. Four examples, illustrating gotten solutions, are given and corresponding stream lines and equipotential lines are represented.
@article{UZKU_2006_148_4_a3,
author = {A. M. Mal'tseva and Yu. V. Obnosov and S. V. Rogozin},
title = {A~generalization of {Milne-Thomson} theorem for the case of annulus},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {35--50},
publisher = {mathdoc},
volume = {148},
number = {4},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a3/}
}
TY - JOUR AU - A. M. Mal'tseva AU - Yu. V. Obnosov AU - S. V. Rogozin TI - A generalization of Milne-Thomson theorem for the case of annulus JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2006 SP - 35 EP - 50 VL - 148 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a3/ LA - ru ID - UZKU_2006_148_4_a3 ER -
%0 Journal Article %A A. M. Mal'tseva %A Yu. V. Obnosov %A S. V. Rogozin %T A generalization of Milne-Thomson theorem for the case of annulus %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2006 %P 35-50 %V 148 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a3/ %G ru %F UZKU_2006_148_4_a3
A. M. Mal'tseva; Yu. V. Obnosov; S. V. Rogozin. A generalization of Milne-Thomson theorem for the case of annulus. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 4, pp. 35-50. http://geodesic.mathdoc.fr/item/UZKU_2006_148_4_a3/