THE STEFAN PROBLEM WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY AND A CONVECTIVE TERM WITH A CONVECTIVE CONDITION AT THE FIXED FACE

被引:5
作者
Briozzo, Adriana C. [1 ,2 ]
Natale, Maria F. [1 ]
Tarzia, Domingo A. [2 ]
机构
[1] Univ Austral, Dept Matemat, FCE, RA-1950 Rosario, Santa Fe, Argentina
[2] Univ Austral, CONICET, FCE, RA-1950 Rosario, Santa Fe, Argentina
关键词
Stefan problem; free boundary problem; moving boundary problem; phase-change process; nonlinear thermal conductivity; fusion; solidification; similarity solution; EQUATION;
D O I
10.3934/cpaa.2010.9.1209
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity and a convective term with a convective boundary condition at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for t >= t(0) > 0 with t(0) an arbitrary positive time. We obtain explicit solutions through the unique solution of a Cauchy problem with the time as a parameter and we also give an algorithm in order to compute the explicit solution.
引用
收藏
页码:1209 / 1220
页数:12
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