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A Stefan problem for a non-classical heat equation with a convective condition by Adriana C. Briozzo; Domingo A. Tarzia is a Mathematics article available to read on EtoBox.

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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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Author

Adriana C. Briozzo; Domingo A. Tarzia

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0096-3003)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)