Optimal regularity for phase transition problems with convection
type: Item
instance of: scholarly article
title: Optimal regularity for phase transition problems with convection
zbMATH Open document ID: 1329.35361
author: A. L. Karakhanyan
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2015-08-31T00:00:00Z
review text: In this paper, the author considers a stationary phase transition problem where the liquid phase is in motion. For given convection \({\mathbf v}\), the problem consists of determining the temperature \(T\) from the equation \[ \Delta T =\mathrm{div}\left({\mathbf v}\beta(T-T_S)\right)+f, \] where \(\beta(s)=as+lH(s)\) is the enthalpy, \(a\) is the specific heat constant, \(l\) is the latent heat constant, \(H\) is the Heaviside function, \(T_S\) is the solidification temperature and \(f\) is a function that accounts for heat sources or sinks. This is also known as Stefan problem with convection and portrays various phase transition models. The main results of this paper state that weak solutions of this problem are locally Lipschitz continuous, provided that \({\mathbf v}=D\xi\), where \(\xi\) is a harmonic function, and the Lipschitz free boundary is \(C^1\) regular when \({\mathbf v}\) is a constant vector (that is, in the case of continuous casting).
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35R37
Mathematics Subject Classification ID: 80A22
zbMATH DE Number: 6476997
zbMATH Keywords: free boundary
zbMATH Keywords: Stefan problem
zbMATH Keywords: phase transition
zbMATH Keywords: convection
zbMATH Keywords: Lipschitz regularity
zbMATH Keywords: viscosity solution
reviewed by: Mariana Vega Smit
MaRDI profile type: Publication
full work available at URL: j.anihpc.2014.03.003
OpenAlex ID: W2018549374
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DOI: 10.1016/J.ANIHPC.2014.03.003
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description: scientific article; zbMATH DE number 6476997