A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face
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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.
论文关键词:Stefan problem,Non-classical heat equation,Free boundary problem,Similarity solution,Nonlinear heat sources,Volterra integral equation
论文评审过程:Available online 15 June 2006.
论文官网地址:https://doi.org/10.1016/j.amc.2006.04.043