Abstract
A family of analytic solutions for a one phase free boundary problem is presented. The model is Hele-Shaw flow with suction where the free boundary can be almost circular initially but develop arbitrarily many cusps in finite time. The analytic solutions are intended as checks for numerical work.
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References
L. Bieberbach, Conformai Mapping, F. Steinhardt, transl., Chelsea Publishing Company, New York 1953.
G. H. Meyer, Hele-Shaw flow with a cusping free boundary, submitted for publication.
J. R. Ockendon, Numerical and analytical solutions of moving boundary problems, in Moving Boundary Problems, D. G. Wilson, A. D. Solomon and P. T. Boggs, edts., Academic Press, New York 1978.
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© 1982 Springer Basel AG
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Meyer, G.H. (1982). Test Solutions for a One Phase Problem through Conformal Transformations. In: Albrecht, J., Collatz, L., Hoffmann, KH. (eds) Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 58. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6563-0_15
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DOI: https://doi.org/10.1007/978-3-0348-6563-0_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6565-4
Online ISBN: 978-3-0348-6563-0
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