Multidimensional two-phase quasistationary Stefan problem
type: Item
instance of: scholarly article
title: Multidimensional two-phase quasistationary Stefan problem
zbMATH Open document ID: 0796.35182
DOI: 10.1007/BF02599314
author: Boris Zaltzman
published in: Manuscripta Mathematica
publication date: 1994-01-31T00:00:00Z
full work available at URL: https://eudml.org/doc/155809
review text: An analysis is being made of a two-dimensional quasi-stationary Stefan problem which is considered as a model problem for the process of crystallization of an infnite ingot moving with a constant velocity with respect to a stationary heat source. The generalized solution of the problem is sought as the limit of a sequence of solutions of the corresponding nonstationary problem when \(t \to \infty\). Existence and uniqueness of the solution are proved, and it is shown that this solution is a classical one. Then, crystallization of a plane ingot with an anisotropic structure (the heat conductivity in the \(x\)-direction is much higher than that in the \(y\)-direction) is modelled. Existence and uniqueness of the solution to the corresponding model problem are also demonstrated. Finally, it is shown that the results obtained can be carried over to three-dimensional problems.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 74A15
zbMATH DE Number: 492764
zbMATH Keywords: crystallization
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Remarks on the quasi-steady one phase Stefan problem
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cites work: Q5186091
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cites work: On the multivalence of a class of meromorphic functions
OpenAlex ID: W2036388146
description: scientific article; zbMATH DE number 492764