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 - <p style="text-align: justify;">In this paper, the two-dimensional slowly rotating highly viscous
fluid flow in small cavities is modelled by the triharmonic equation
for the streamfunction. &nbsp;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. &nbsp;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.</p>