Electron. J. Differential Equations, Vol. 2020 (2020), No. 49, pp. 1-14.

Supercooled Stefan problem with a Neumann type boundary condition

Adriana C. Briozzo

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.
DOI: 10.58997/ejde.2020.49

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Adriana C. Briozzo
CONICET and Depto. Matemática
FCE, Univ. Austral
Paraguay 1950, S2000FZF Rosario, Argentina
email: abriozzo@austral.edu.ar

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