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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 ,
S. V. ROGOSIN  and
F. HÜBNER
M. REISSIG
Affiliation:
Faculty of Mathematics and Computer Science TU Bergakademie Freiberg, Bernhard von Cotta Str. 2, 09596 Freiberg, Germany (email: [email protected])
S. V. ROGOSIN
Affiliation:
Faculty of Mathematics and Mechanics, Belarusian State University, F.Skaryny av. 4, 220050 Minsk, Belarus (email: [email protected])
F. HÜBNER
Affiliation:
Faculty of Mathematics and Computer Science TU Bergakademie Freiberg, Bernhard von Cotta Str. 2, 09596 Freiberg, Germany (email: [email protected])
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Abstract

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
Information
European Journal of Applied Mathematics , Volume 10 , Issue 6 , December 1999 , pp. 561 - 579
Copyright
© 1999 Cambridge University Press

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