Volume 1, Issue 1
On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow

Adv. Appl. Math. Mech., 1 (2009), pp. 140-150.

Published online: 2009-01

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• Abstract

In this paper, the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.  The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however, do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain.  This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy. The analysis is further generalized to polyharmonic equations.

• Keywords

Boundary integral equations, triharmonic and polyharmonic equations, logarithmic capacity.

• AMS Subject Headings

31A30, 31B10

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• TXT
@Article{AAMM-1-140, author = {D. and Lesnic and and 20651 and and D. Lesnic}, title = {On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {1}, pages = {140--150}, abstract = {

In this paper, the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.  The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however, do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain.  This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy. The analysis is further generalized to polyharmonic equations.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/213.html} }
TY - JOUR T1 - On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow AU - Lesnic , D. JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 140 EP - 150 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/213.html KW - Boundary integral equations, triharmonic and polyharmonic equations, logarithmic capacity. AB -

In this paper, the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.  The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however, do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain.  This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy. The analysis is further generalized to polyharmonic equations.

D. Lesnic. (1970). On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow. Advances in Applied Mathematics and Mechanics. 1 (1). 140-150. doi:
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