The Stefan problem with temperature-dependent thermal conductivity and aconvective term with a convective condition at the fixed face
Adriana C. Briozzo, María Fernanda Natale, Domingo Alberto Tarzia · Communications on Pure & Applied Analysis · 2010
We study a one-phase Stefan problem for a semi-infinitematerial with temperature-dependent thermal conductivity and aconvective term with a convective boundary condition at the fixedface $x=0$. We obtain sufficient conditions for data in orderto have a parametric representationof the solution of the similarity type for $t \geq t_0 > 0$ with $t_0 $ an arbitrary positive time. We obtain explicitsolutions through the unique solution of a Cauchy problem with thetime as a parameter and we also give an algorithm in order tocompute the explicit solution.