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

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.

Auxiliary functions in the study of Stefan-like problems with variable thermal properties

“…Analogous methods were also used to determine solutions to problems with more general thermal coefficients, see e.g. [10,11]. Other approaches to find similarity solutions to Stefanlike problems with non-constant thermal properties and arbitrary initial and boundary conditions were recently considered in, e.g., [12][13][14][15][16].…”

Explicit solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

“…Existence and uniqueness to the problem (1.1)-(1.5) with null source term, H = 0, was developed in [5].…”

Stefan problems for the diffusion–convection equation with temperature-dependent thermal coefficients

“…where q > 0 is a given constant and − q √ t represents the prescribed flux at x = 0. Some bibliography imposing this kind of condition can be found in [18,19,20,21,22] On the other hand, we consider a problem governed by (1a) and (1c)-(1e) where a Robin condition is imposed:…”