Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 21, pp. 1-16.
Title: Existence and uniqueness for one-phase Stefan problems
of non-classical heat equations with temperature
boundary condition at a fixed face
Authors: Adriana C. Briozzo (Univ. Austral, Rosario, Argentina)
Domingo A. Tarzia (Univ. Austral, Rosario, Argentina)
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.