Work

A transform approach to the supercooled Stefan problem

Year: 2026

Type: article

Abstract: We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from [4] allowing for non-integrable initial data. From an application of Ito’s formula, we obtain a relationship between the Laplace transform of the initial data and a transform of the solution, together with its possibly discontinuous free boundary. Using this relationship we give a sharp existence result for global solutions, we extend previous results on the uniqueness of solutions, and we determine the asymptotic behaviour of solutions for a certain class of initial data.

Source: Electronic Communications in Probability

DOI: 10.1214/26-ecp814

Authors: Thomas Blore, Ben Hambly

Institution: University of Oxford

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Engineering and Physical Sciences Research Council

Award: EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation