OPTIMAL L1-TYPE RELAXATION RATES FOR THE CAHN-HILLIARD EQUATION ON THE LINE

被引：4
作者：
Otto, Felix [1 ]
Scholtes, Sebastian [2 ]
Westdickenberg, Maria G. [2 ]
机构：
[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[2] Rhein Westfal TH Aachen, Templergraben 55, D-52062 Aachen, Germany
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 06期
关键词：
energy-energy-dissipation; nonlinear PDE; gradient flow; relaxation rates; STABILITY; FRONTS;
D O I：
10.1137/18M1192640
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance in terms of either a first moment or the excess mass-to a kink profile and capture the decay rate of the energy and the perturbation. Our tools include Nash-type inequalities, duality arguments, and Schauder estimates.
引用
收藏
页码：4645 / 4682
页数：38
相关论文
共 15 条
12