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.