Explicit solutions for a two-phase unidimensional Lamé-Clapeyron-Stefan problem with source terms in both phases
type: Item
instance of: scholarly article
title: Explicit solutions for a two-phase unidimensional Lamé-Clapeyron-Stefan problem with source terms in both phases
zbMATH Open document ID: 1129.35083
author: Adriana C. Briozzo
author: María F. Natale
author: Domingo A. Tarzia
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-26T00:00:00Z
review text: The authors consider the classical Stefan problem with different thermal coefficients in the two phases and also different heat sources depending on the variable \(\frac{x}{ra_i\sqrt{t}}\) in the solid phase \((i=1)\) and liquid phase \((i=2)\), \(a_i\) denoting heat diffusivity. The problem is formulated for \(x>0\), \(t>0\). The initial temperature is a negative constant (phase change temperature is zero) and the same value is imposed for \(x\rightarrow +\infty\). Explicit solutions are constructed when at \(x=0\) temperature is prescribed as a positive constant and when incoming heat flux is given with an \(1/\sqrt{t}\) singularity. Conditions ensuring the equivalence of these two classes are analyzed together with other properties of the solutions.
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 5129639
zbMATH Keywords: Stefan problem
zbMATH Keywords: Lamé-Clapeyron solution
zbMATH Keywords: Neumann solution
zbMATH Keywords: phase-change
zbMATH Keywords: sublimation-dehydration similarity solution
reviewed by: Antonio Fasano
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.05.083
OpenAlex ID: W2012778847
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DOI: 10.1016/J.JMAA.2006.05.083
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description: scientific article; zbMATH DE number 5129639