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

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2010年 / 9卷 / 05期

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

页码：1209 / 1220

页数：12

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