A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition
Analysis of PDEs
2025-10-31 v1
Abstract
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay, global-in-time solutions with non-exponential decay, and finite-time blow-up solutions. The classification depends on the size of the initial function. Furthermore, we describe the behavior of solutions at the blow-up time.
Cite
@article{arxiv.2510.26088,
title = {A one-dimensional Stefan problem for the heat equation with a nonlinear boundary condition},
author = {Kensho Araya and Kazuhiro Ishige},
journal= {arXiv preprint arXiv:2510.26088},
year = {2025}
}