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

## TL;DR

This paper investigates the existence and uniqueness of solutions for one-dimensional Stefan problems with temperature-dependent thermal coefficients, analyzing different boundary conditions and their convergence, supported by computational examples.

## Contribution

It establishes conditions for existence and uniqueness of solutions and demonstrates the convergence of Robin to Dirichlet boundary conditions in Stefan problems.

## Key findings

- Existence and uniqueness of solutions are proven.
- Solutions with Robin conditions converge to Dirichlet solutions.
- Computational examples illustrate theoretical results.

## 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.