Year: 2009
Author: D. Lesnic
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-213
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 1 : pp. 140–150
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Boundary integral equations triharmonic and polyharmonic equations logarithmic capacity.