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Analytical and numerical treatment of a complex model for Hele-Shaw moving boundary value problems with kinetic undercooling regularization

Published online by Cambridge University Press:  01 December 1999

M. REISSIG
Affiliation:
Faculty of Mathematics and Computer Science TU Bergakademie Freiberg, Bernhard von Cotta Str. 2, 09596 Freiberg, Germany (email: reissig@mathe.tu-freiberg.de)
S. V. ROGOSIN
Affiliation:
Faculty of Mathematics and Mechanics, Belarusian State University, F.Skaryny av. 4, 220050 Minsk, Belarus (email: rogosin@mmf.bsu.unibel.by)
F. HÜBNER
Affiliation:
Faculty of Mathematics and Computer Science TU Bergakademie Freiberg, Bernhard von Cotta Str. 2, 09596 Freiberg, Germany (email: reissig@mathe.tu-freiberg.de)
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Abstract

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In this paper, a complex variable model for Hele-Shaw moving boundary problems with kinetic undercooling regularization is studied. This model consists of an abstract Cauchy–Kovalevsky problem and of a Riemann–Hilbert–Poincaré problem for holomorphic functions. The local existence of holomorphic solutions is shown. Some numerical results for this model complete the paper.

Type
Research Article
Copyright
© 1999 Cambridge University Press