A Convergence result for a Stefan problem with phase relaxation

TL;DR

This paper proves that solutions of a phase relaxation model for the Stefan problem converge strongly to the classical Stefan problem's solutions as the relaxation parameter approaches zero, under general boundary conditions.

Contribution

It establishes a convergence result for a phase relaxation model of the Stefan problem with more general boundary conditions, extending previous analyses.

Findings

Solution converges strongly to the classical Stefan problem

Convergence holds under more general boundary conditions

Provides a rigorous asymptotic analysis for phase relaxation

Abstract

In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural physical assumption that the initial condition of the phase is constrained, but taking more general boundary conditions, we prove that the solution of this relaxed model converges in a stronger way to the solution of the classical weak Stefan problem.