Preprint
Refine
Year of publication
- 1999 (1)
Document Type
- Preprint (1) (remove)
Language
- English (1)
Has Fulltext
- yes (1)
Keywords
- Theorem of Plemelj-Privalov (1) (remove)
Faculty / Organisational entity
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.