TY - INPR
A1 - Götz, Thomas
A1 - Unterreiter, Andreas
T1 - On an Integral Equation Model for Slender Bodies in Low Reynolds-Number Flows
N2 - The interation of particular slender bodies with low Reynolds-number flows is in the limit 'slenderness to 0' described by a linear Fredholm integral equation of the second kind. The integral operator of this equation has a denumerable set of polynomial eigenfunctions whose corresponding eigenvalues are non-positive and of logarithmic growth. A theorem similiar to a classical result of Plemelj-Privalov for integral operators with Cauchy kernels is proven. In contrast to Cauchy kernel operators, the integral operator maps no Hölder space into itself. A spectral analysis of the integral operator restricted to an appropriate class of analytic functions is performed. The spectral properties of this restricted integral operator suggest a collocation-like method to solve the integral equation numerically. For this numerical scheme, convergence is proven and several computations are presented.
T3 - Berichte der Arbeitsgruppe Technomathematik (AGTM Report) - 219
KW - Fredholm integral equation of the second kind
KW - Theorem of Plemelj-Privalov
KW - Spectral Analysis
KW - Polynomial Eigenfunctions
KW - Collocation Method plus
Y1 - 1999
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1044
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-9978
ER -