LARGE-TIME BEHAVIOR FOR A PHASE-FIELD SYSTEM OF 3D-GRAIN BOUNDARY MOTION

被引：0
|
作者：
Moll, Salvador [1 ]
Shirakawa, Ken [2 ]
Watanabe, Hiroshi [3 ]
机构：
[1] Univ Valencia, Dept Anal Matemat, C Dr Moliner 50, Burjassot, Spain
[2] Chiba Univ, Fac Educ, Dept Math, 1-33 Yayoi Cho,Inage Ku, Chiba 2638522, Japan
[3] Oita Univ, Fac Sci & Technol, Dept Integrated Sci & Technol, 700 Dannoharu, Oita 8701192, Japan
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 05期
关键词：
parabolic system; grain boundary motion; orientations; total variation; omega- limit set; P-HARMONIC MAPS; CENTER-OF-MASS; GRAIN; EXISTENCE; MODEL; SETS;
D O I：
10.1137/23M1571988
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a three dimensional model for grain boundary motion with the presence of time-dependent external forces. We show existence of solutions in the large. We also show that the \omega- limit set of the solutions is compact and that the \omega- limit points satisfy the corresponding elliptic system. In the case of no external forcing for the rotation and, under a condition on the range of the initial datum, we prove that the system reaches a steady state in a finite time and that, in this case, the rotation becomes a constant one.
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页码：6885 / 6914
页数：30
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