On the successive approximation of classical solutions for multi-surface free-boundary problems with general non-linear joining conditions

Andrew Acker

Vol. 188 (1999), No. 1, 1–51

DOI: 10.2140/pjm.1999.188.1

Abstract

We prove the global convergence of an analytical trial free-boundary algorithm, called the operator method, in the context of a very large class of multiple-free-boundary problems in ℝ^N, N ≥ 2. We study the general case of a finite number of annular flow-layers, having a nested family of closed, (N − 1)-dimensional hypersurfaces as interfaces. Each interface is characterized by a general non-linear joining condition relating the normal derivatives of the stream functions in the two adjoining layers.

Milestones

Received: 21 April 1997

Revised: 5 January 1998

Published: 1 March 1999