A Stefan problem for a non-classical heat equation with a convective condition |
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Authors: | Adriana C. Briozzo |
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Affiliation: | Depto. Matemática, F.C.E., Universidad Austral and CONICET, Paraguay 1950, S2000FZF Rosario, Argentina |
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Abstract: | 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 convective boundary condition at the fixed face x = 0. Here the heat source depends on the temperature at the fixed face x = 0 that provides a heating or cooling effect depending on the properties of the source term. 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. We also obtain a comparison result of the solution (the temperature and the free boundary) with respect to the one corresponding with null source term. |
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Keywords: | Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation |
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