A new convergence proof for approximations of the Stefan problem

TL;DR

This paper provides a new convergence proof for approximations of the Stefan problem, applicable to both regular and irregular data, using weak formulations and compactness in Sobolev spaces.

Contribution

It introduces a novel convergence proof for Stefan problem approximations that handles irregular data through advanced functional analysis techniques.

Findings

Convergence proven for regular data cases.

Convergence proven for irregular data cases.

Uses weak formulations and Sobolev space compactness.

Abstract

We consider the Stefan problem, firstly with regular data and secondly with irregular data. In both cases is given a proof for the convergence of an approximation obtained by regularising the problem. These proofs are based on weak formulations and on compactness results in some Sobolev spaces with negative exponents.