## On an Integral Equation Model for Slender Bodies in Low Reynolds-Number Flows

• 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.

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Author: Thomas Götz, Andreas Unterreiter urn:nbn:de:hbz:386-kluedo-9978 Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (219) Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/02/25 Collocation Method plus; Fredholm integral equation of the second kind ; Polynomial Eigenfunctions ; Spectral Analysis ; Theorem of Plemelj-Privalov Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

$Rev: 13581$