Regularity of the free boundary in parabolic phase-transition problems
Regularity of the free boundary in parabolic phase-transition problems
复制标题
抛物线相变问题中自由边界的规律性
DOI：
10.1007/bf02551583
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发表时间：
1996
期刊：
影响因子：
3.7
通讯作者：
S. Salsa
中科院分区：
文献类型：
--
作者：
I. Athanasopoulos;L. Caffarelli;S. Salsa
本文研究了抛物型两相自由边界问题自由边界的正则性。抛物型两相自由边界问题最著名的例子可能是Stefan问题，这是一个描述具有固-液界面的材料熔化（或凝固）的简化模型。解的概念可以用几种方式表述（经典解、发散形式的弱解或粘性解），通常，人们想证明可能构造的（弱）解实际上是尽可能光滑和经典的。Stefan问题的一个经典局部解可以描述如下：在单位圆柱Q1 =B1“（-1，1）上，我们有两个互补区域Q1和Q2，它们被光滑曲面S=（O 1 ~ 2）NQ 1分隔开。在f1和Q1中，我们有热方程的两个光滑解，U1和u2，
In this paper we start the study of the regularity properties of the free boundary, for parabolic two-phase free boundary problems. May be the best known example of a parabolic two-phase free boundary problem is the Stefan problem, a simplified model describing the melting (or solidification) of a material with a solid-liquid interphase. The concept of solution can be stated in several ways (classical solution, weak so- lution on divergence form, or viscosity solution) and as usual, one would like to prove that the (weak) solutions that may be constructed, are in fact as smooth and classical as possible. Locally, a classical solution of the Stefan problem may be described as following: On the unit cylinder Q1 =B1 “ (-1, 1) we have two complementary domains, ~ and QI\~, separated by a smooth surface S=(OI2)NQ1. In fl and QI\~ we have two smooth solutions, Ul and u2, of the heat equations