A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face

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• 作者：Adriana C. Briozzo ; Domingo A. Tarzia
• 关键词：Stefan problem ; Non-classical heat equation ; Free boundary problem ; Similarity solution ; Nonlinear heat sources ; Volterra integral equation
• 刊名：Applied Mathematics and Computation
• 出版年：2006
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 November 2006
• 卷：182
• 期：1
• 页码：809-819
• 文件大小：198 K

摘要

We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a heat flux boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0. We use the Friedman–Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.