Uniqueness for solutions of the two-phase Stefan problem with signed measures as data

TL;DR

This paper proves the uniqueness of solutions to the two-phase Stefan problem when initial data are signed measures, advancing the mathematical understanding of phase transition models with irregular initial conditions.

Contribution

It establishes the first uniqueness results for the two-phase Stefan problem with signed measure initial data, broadening the class of initial conditions for which solutions are well-posed.

Findings

Uniqueness of solutions with signed measure initial data.

Extension of well-posedness results to irregular initial conditions.

Mathematical framework for phase transition problems with signed measures.

Abstract

We show uniqueness of solutions to the two-phase Stefan problem which have signed measures as initial data.