Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients

Julieta Bollati; María Fernanda Natale; José Abel Semitiel; Domingo Alberto Tarzia

doi:10.1016/j.nonrwa.2019.103001

paper

Existence and uniqueness of solution for two one-phase Stefan problems with variable thermal coefficients

arXiv:1903.10340 · doi:10.1016/j.nonrwa.2019.103001

Abstract

One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face $x = 0$ . Moreover, it is proved that the solution of the problem with the Robin type condition converges to the solution of the problem with the Dirichlet condition at the fixed face. Computational examples are provided.

11 pages, 5 figures