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Non-linear singular integral equations on a finite interval

✍ Scribed by P. Junghanns; G. Semmler; U. Weber; E. Wegert

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
212 KB
Volume
24
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A class of nonlinear singular integral equations of Cauchy type on a finite interval is transformed to an equivalent class of (discontinuous) boundary value problems for holomorphic functions in the complex unit disk. Using recent results on the solvability of explicit Riemann–Hilbert problems, we prove the existence of solutions to the integral equation with bounded piecewise continuous nonlinearities. We discuss the influence of parameters and additional conditions and demonstrate the approach for a free boundary problem arising from seepage near a channel. Copyright © 2001 John Wiley & Sons, Ltd.

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