Regularity of the free boundary for a parabolic cooperative system

被引：3

作者：

Aleksanyan, G. ^{[1
]}

Fotouhi, M. ^{[2
]}

Shahgholian, H. ^{[3
]}

Weiss, G. S. ^{[4
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[2] Sharif Univ Technol, Dept Math Sci, Tehran, Iran

[3] Royal Inst Technol, Dept Math, Stockholm, Sweden

[4] Univ Duisburg Essen, Dept Math, Essen, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 61卷 / 04期

基金：

瑞典研究理事会; 美国国家科学基金会;

关键词：

SET;

D O I：

10.1007/s00526-022-02244-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the following parabolic system Delta u - partial derivative(t)u = vertical bar u vertical bar(q-1) u chi({vertical bar u vertical bar > 0}), = (u(1), ... , u(m)), with free boundary partial derivative{vertical bar u vertical bar > 0). For 0 <= q < 1, we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C-1,C-alpha in space directions and half-Lipschitz in the time direction.

引用

页数：38

共 12 条

[1] Equilibrium points of a singular cooperative system with free boundary [J].