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.

引用

页码：6885 / 6914

页数：30

共 50 条

[21] Phase-field study of pore-grain boundary interaction
Hoetzer, Johannes
Rehn, Veronika
Rheinheimer, Wolfgang
Hoffmann, Michael J.
Nestler, Britta
JOURNAL OF THE CERAMIC SOCIETY OF JAPAN, 2016, 124 (04) : 329 - 339
[22] Thermodynamic properties of phase-field models for grain boundary segregation
Kim, Seong Gyoon
Lee, Jae Sang
Lee, Byeong-Joo
ACTA MATERIALIA, 2016, 112 : 150 - 161
[23] Solute segregation in a moving grain boundary: a phase-field approach
Guin, Sandip
Verma, Miral
Bandyopadhyay, Soumya
Lo, Yu-Chieh
Mukherjee, Rajdip
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, 2024, 32 (06)
[24] Large-time asymptotic behavior for the classical thermoelastic system
Chen, Wenhui
Takeda, Hiroshi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 377 : 809 - 848
[25] Molecular dynamics simulations on grain-boundary behavior and its application to phase-field modeling
Uehara, Takuya
Hirabayashi, Yoshitaka
Ohno, Nobutada
MECHANICAL BEHAVIOR OF MATERIALS X, PTS 1AND 2, 2007, 345-346 : 971 - +
[26] LARGE-TIME BEHAVIOR OF SOLUTIONS TO A DISSIPATIVE BOUSSINESQ SYSTEM
Abounouh, M.
Atlas, A.
Goubet, O.
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2007, 20 (07) : 755 - 768
[27] An existence and uniqueness result for a phase-field model of diffusion-induced grain-boundary motion
Deckelnick, K
Elliott, CM
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2001, 131 : 1323 - 1344
[28] GLOBAL SOLUTIONS TO AN INITIAL-BOUNDARY VALUE PROBLEM OF A PHASE-FIELD MODEL FOR MOTION OF GRAIN BOUNDARIES
Bian, Xingzhi
Zhu, Peicheng
Guo, Boling
Zhang, Ping
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2024, 56 (04) : 4296 - 4323
[29] ASYMPTOTIC BEHAVIOR OF THE CAGINALP PHASE-FIELD SYSTEM WITH COUPLED DYNAMIC BOUNDARY CONDITIONS
Conti, Monica
Gatti, Stefania
Miranville, Alain
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2012, 5 (03): : 485 - 505
[30] Global existence and large-time behavior for primitive equations with the free boundary
HaiLiang Li
Chuangchuang Liang
ScienceChina(Mathematics), 2024, 67 (10) : 2303 - 2330

← 1 2 3 4 5 →