Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 49, pp. 1-14.

Title: Supercooled Stefan problem with a Neumann type boundary condition
       
Author: Adriana C. Briozzo (CONICET, Rosario, Argentina)

Abstract:
 We consider a  supercooled one-dimensional Stefan problem with a Neumann boundary
 condition and  a variable thermal diffusivity. We establish a necessary and sufficient
 condition for the heat flux  at  the fixed face x=0,
 in order to obtain existence and uniqueness of a similarity type solution.
 Moreover we over-specified the fixed face x=0 by a Dirichlet boundary condition
 aiming at the simultaneous determination of one or two thermal coefficients.
 
Submitted January 9, 2020. Published May 22, 2020.
Math Subject Classifications: 35R35, 80A22, 35K55.
Key Words: Stefan problem; supercooling; non-linear thermal diffusivity;
           similarity solution; determination of thermal coefficient.