On solutions of an ill-posed Stefan problem

TL;DR

This paper investigates a multi-phase Stefan problem with complex initial data and negative latent heats, proposing a variational approach to determine conditions for the existence and uniqueness of self-similar solutions.

Contribution

It introduces a variational formulation for self-similar solutions in a multi-phase Stefan problem with negative latent heats, providing new existence and uniqueness criteria.

Findings

Derived conditions for solution existence

Established uniqueness of self-similar solutions

Extended analysis to negative latent heats

Abstract

We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find precise conditions for existence and uniqueness of the solution.