Well-posedness for a two-phase Stefan problem with radiation

2025/05/30 by Demattè, Elena, Velázquez, Juan J. L. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.24602

Abstract

In this paper we consider a free boundary problem for the melting of ice where we assume that the heat is transported by conduction in both the liquid and the solid part of the material and also by radiation in the solid. Specifically, we study a one-dimensional two-phase Stefan-like problem which contains a non-local integral operator in the equation describing the temperature distribution of the solid. We will prove the local well-posedness of this free boundary problem combining the Banach fixed-point theorem and classical parabolic theory. Moreover, constructing suitable stationary sub- and supersolutions we will develop a global well-posedness theory for a large class of initial data.

Citations

• Equilibrium and Non-Equilibrium diffusion approximation for the radiative transfer equation
• Compactness and existence theory for a general class of stationary radiative transfer equations
• On the diffusion approximation of the stationary radiative transfer equation with absorption and emission
• On the temperature distribution of a body heated by radiation
• Radiative Transfer in a Fluid
• Free Boundary Problems for Parabolic Equations I. Melting of Solids

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• Traveling waves for a two-phase Stefan problem with radiation

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