Adriana C. Briozzo, Domingo A. Tarzia
Abstract:
We prove the existence and uniqueness, local in time, of a
solution for a one-phase Stefan problem of a non-classical
heat equation for a semi-infinite material with temperature
boundary condition at the fixed face.
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.
Submitted November 1, 2005. Published February 9, 2006.
Math Subject Classifications: 35R35, 80A22, 35C05, 35K20, 35K55, 45G15, 35C15.
Key Words: Stefan problem; non-classical heat equation;
free boundary problem; similarity solution; nonlinear heat sources;
Volterra integral equations.
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Adriana C. Briozzo Departamento de Matemática FCE, Universidad Austral Paraguay 1950, S2000FZF Rosario, Argentina email: Adriana.Briozzo@fce.austral.edu.ar |
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Domingo Alberto Tarzia Departamento de Matemática - CONICET FCE, Universidad Austral Paraguay 1950, S2000FZF Rosario, Argentina email: Domingo.Tarzia@fce.austral.edu.ar |
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