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Non‐linear singular integral equations on a finite interval
Author(s) -
Junghanns P.,
Semmler G.,
Weber U.,
Wegert E.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.272
Subject(s) - mathematics , mathematical analysis , interval (graph theory) , singular integral , holomorphic function , nonlinear system , bounded function , boundary value problem , integral equation , piecewise , singular solution , class (philosophy) , unit disk , boundary (topology) , physics , quantum mechanics , combinatorics , artificial intelligence , computer science
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.