Electron. J. Diff. Eqns., Vol. 2006(2006), No. 21, pp. 1-16.

Existence and uniqueness for one-phase Stefan problems of non-classical heat equations with temperature boundary condition at a fixed face

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
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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