Differential and Integral Equations

Two Stefan problems for a non-classical heat equation with nonlinear thermal coefficients

Adriana C. Briozzo and María Fernanda Natale

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The mathematical analysis of two one-phase unidimensional and non-classical Stefan problems with nonlinear thermal coefficients is obtained. Two related cases are considered, one of them has a temperature condition on the fixed face $x=0$ and the other one has a flux condition of the type $-q_{0}/\sqrt{t }$ $ ( q_{0}>0 ) .$ In the first case, the source function depends on the heat flux at the fixed face $x=0,$ and in the other case it depends on the temperature at the fixed face $x=0. $ In both cases, we obtain sufficient conditions in order to have the existence of an explicit solution of a similarity type, which is given by using a double fixed point.

Article information

Differential Integral Equations, Volume 27, Number 11/12 (2014), 1187-1202.

First available in Project Euclid: 18 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems 80A22: Stefan problems, phase changes, etc. [See also 74Nxx] 45G10: Other nonlinear integral equations


Briozzo, Adriana C.; Natale, María Fernanda. Two Stefan problems for a non-classical heat equation with nonlinear thermal coefficients. Differential Integral Equations 27 (2014), no. 11/12, 1187--1202. https://projecteuclid.org/euclid.die/1408366789

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