Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling
type: Item
instance of: scholarly article
title: Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling
zbMATH Open document ID: 0761.35113
DOI: 10.1016/0022-247X(92)90119-X
author: Xinfu Chen
author: F. Reitich
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The paper studies a modified Stefan problem which includes the ``modified Gibbs-Thomson relation'' on the free surface separating the solid and liquid phases. On the interface, the temperature \(u\) satisfies \(u=\sigma K-\beta V\), where \(K\) and \(V\) are the mean curvature and the normal velocity of the interface, respectively. Short term existence and uniqueness of classical solutions of the free boundary problem are obtained.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 62042
zbMATH Keywords: short time existence
zbMATH Keywords: modified Gibbs-Thomson relation
reviewed by: Suzanne Lenhart
MaRDI profile type: Publication
cites work: Generation and Propagation of Interfaces in Reaction-Diffusion Systems
cites work: Dynamics of interfaces in reaction diffusion systems
cites work: Exact evaluation of the Green function for the anisotropic simple cubic lattice
cites work: Q3678248
cites work: Classical solutions of the Stefan problem
cites work: Solutions for the two-phase Stefan problem with the Gibbs–Thomson Law for the melting temperature
cites work: Q3891123
cites work: Q3677325
description: scientific article; zbMATH DE number 62042