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

M. REISSIG; S. V. ROGOSIN; F. HÜBNER

doi:10.1017/S0956792599003939

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.

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

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