Zusammenfassung
Wir zeigen, wie der freie Rand einer idealen Flüssigkeit, welcher einer verallgemeinerten Bernoulli-Bedingung genügt, unter geeigneten Umständen approximiert werden kann. Unsere Methode stützt sich auf eine Klasse freier RandperturbationsoperatorenT ε, 0<ε<1, welche relativ zu einer geeigneten Norm und Ränderklasse kontrahierend sind und deren Fixpunkte gegen die gewünschte Lösung der freien Randaufgabe mitε → 0+ konvergieren.
Abstract
We show how the free boundary of an ideal fluid, subject to a generalized Bernoulli condition, can (under appropriate circumstances) be approximated. Our method is based on a class of free-boundary perturbation operatorsT ε, 0<ε<1, which are all contracting relative to a suitable norm and class of boundaries, and whose fixed points converge to the desired free boundary solution asε → 0+.
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Acker, A. How to approximate the solutions of certain free boundary problems for the Laplace equation by using the contraction principle. Z. angew. Math. Phys. 32, 22–33 (1981). https://doi.org/10.1007/BF00953547
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DOI: https://doi.org/10.1007/BF00953547