Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T12:32:10.727Z Has data issue: false hasContentIssue false

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)

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
Copyright
© 1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)