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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.
Verfasser*innenangaben: | Thomas Götz, Andreas Unterreiter |
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URN: | urn:nbn:de:hbz:386-kluedo-9978 |
Schriftenreihe (Bandnummer): | Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (219) |
Dokumentart: | Preprint |
Sprache der Veröffentlichung: | Englisch |
Jahr der Fertigstellung: | 1999 |
Jahr der Erstveröffentlichung: | 1999 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Datum der Publikation (Server): | 25.02.2000 |
Freies Schlagwort / Tag: | Collocation Method plus; Fredholm integral equation of the second kind; Polynomial Eigenfunctions; Spectral Analysis; Theorem of Plemelj-Privalov |
Fachbereiche / Organisatorische Einheiten: | Kaiserslautern - Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |