标题： 关于辐射的两相Stefan问题的行波 显示英文标题

标题： Traveling waves for a two-phase Stefan problem with radiation

摘要： 本文研究了一类自由边界问题中行波解的存在性，该问题描述了一种材料相变的过程，其中热的传输既包括导热也包括辐射。 具体来说，我们考虑了一个一维两相Stefan问题，并额外引入了一个非局部非线性积分项，用于描述固体相中热通过辐射传递的情况，而液体相完全透明，不与辐射相互作用。 我们将证明，所考虑的模型存在行波解，这与经典Stefan问题中的情况不同，在后者中仅存在具有抛物尺度的自相似解$ x\sim \sqrt{t} $。 特别是，我们将展示出固体膨胀的行波解的存在性。 这些解的性质将通过最大值原理方法、爆破极限以及非线性积分-微分方程的Liouville型定理来研究。 显示英文摘要

摘要： In this paper we study the existence of traveling wave solutions for a free-boundary problem modeling the phase transition of a material where the heat is transported by both conduction and radiation. Specifically, we consider a one-dimensional two-phase Stefan problem with an additional non-local non-linear integral term describing the situation in which the heat is transferred in the solid phase also by radiation, while the liquid phase is completely transparent, not interacting with radiation. We will prove that there are traveling wave solutions for the considered model, differently from the case of the classical Stefan problem in which only self-similar solutions with the parabolic scale $ x\sim \sqrt{t} $ exist. In particular we will show that there exist traveling waves for which the solid expands. The properties of these solutions will be studied using maximum-principle methods, blow-up limits and Liouville-type Theorems for non-linear integral-differential equations.