A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

doi:10.1016/S0252-9602(09)60098-9

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1216-1224.doi: 10.1016/S0252-9602(09)60098-9

A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

刘长春, 周娟, 尹景学

1.Department of Mathematics, Jilin University, Changchun, 130012, China
2.Institute of System Science, Northeastern University, Shenyang 110004, China

收稿日期:2007-07-29 出版日期:2009-09-20 发布日期:2009-09-20
基金资助:
Supported by NSF of China

A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

LIU Chang-Chun, ZHOU Juan, YIN Jing-Xue

Received:2007-07-29 Online:2009-09-20 Published:2009-09-20
Supported by:
Supported by NSF of China

摘要/Abstract

摘要：

This article is devoted to the discussion of large time behaviour of solutions for viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Some results on global existence of weak solutions for small initial value and
blow-up of solutions for any nontrivial initial value are established.

关键词: Cahn Hilliard equation, existence, blow up

Abstract:

Key words: Cahn Hilliard equation, existence, blow up

中图分类号:

35B65

刘长春, 周娟, 尹景学. A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION[J]. 数学物理学报(英文版), 2009, 29(5): 1216-1224.

LIU Chang-Chun, ZHOU Juan, YIN Jing-Xue. A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1216-1224.

参考文献

[1] Novick-Cohen A. On the viscous Cahn-Hilliard equation//Ball J, ed. Material Instabilities in Continuum Mechanics and Related Mathematical Problems. Oxford: Oxford Science Publications, Clarendon Press,
1988: 329--342

[2] Reyna L G, Ward M J. Meatball internal layer dynamics for the viscous Cahn-Hilliard equation. Methods and Applications of Analysis, 1995, 2: 285--306

[3] Novick-Cohen A, Pego R L. Stable patterns in a viscous diffusion equation. Trans Amer Math Soc, 1991, 324: 331--351

[4] Elliott C M, Garcke H. On the Cahn-Hilliard equation with degenerate mobility. SIAM J Math Anal, 1996, 27: 404--423

[5] Elliott C M, Zheng S M. On the Cahn-Hilliard equation. Arch Rat Mech Anal, 1986, 96: 339--357

[6] Elliott C M, Stuart A M. The viscous Cahn-Hilliard equation: part II analysis. J Differ Equ, 1996, 128: 387--414

[7] Zheng Songmu. Asymptotic behavior of solution to the Cahn-Hilliard equation. Appl Anal, 1986, 23: 165--184

[8] Dlotko T. Global attractor for the Cahn-Hilliard equation in H² and H³. J Differ Equ, 1994, 113: 381--393

[9] Elliott C M, Kostin I N. Lower semicontinuity of a non-hyperbolic attractor for the viscous Cahn-Hilliard equation.
Nonlinearity, 1996, 9: 687--702

[10] Liu Changchun, Yin Jingxue. Some properties of solution s for viscous Cahn-Hilliard equation. Northeast Math J, 1998, 14: 455--466

[11] Ke Yuanyuan, Yin Jingxue. A note on the viscous Cahn-Hilliard equation. Northeast Math J, 2004, 20: 101--108

[12] Huang Rui, Yin Jingxue, Li Yinghua, Wang Chunpeng. Global existence and blow-up of solutions to multi-dimensional (n ≤ 5) viscous Cahn-Hillaird equation. Northeast Math J, 2005, 21: 371--378

[13] Fu Yiping, Guo Boling. Almost periodic solution of one dimensional viscous Camassa-Holm equation. Acta Math Sci, 2007, 27B(1): 117--124

[1]	Xianmei ZHOU. NONEXISTENCE AND EXISTENCE OF SUPERSOLUTIONS FOR HIGHER ORDER SEMILINEAR EQUATIONS IN EXTERIOR DOMAINS[J]. 数学物理学报(英文版), 2025, 45(5): 1920-1941.
[2]	Siyan GUO, Jiangbo HAN, Runzhang XU. WELL-POSEDNESS OF 2-D HYPERBOLIC VISCOUS CAHN-HILLIARD EQUATION[J]. 数学物理学报(英文版), 2025, 45(4): 1438-1470.
[3]	Qingyan LI, Zhenhua GUO. GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS[J]. 数学物理学报(英文版), 2025, 45(3): 951-981.
[4]	Yue ZHANG, Minyan YU, Houzhi TANG. GLOBAL STRONG SOLUTION OF THE PRESSURELESS NAVIER-STOKES/NAVIER-STOKES SYSTEM[J]. 数学物理学报(英文版), 2025, 45(3): 1045-1062.
[5]	Qiangchang JU, Jianjun XU. LONG TIME EXISTENCE FOR THE NON-ISENTROPIC SLIGHTLY COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE[J]. 数学物理学报(英文版), 2025, 45(2): 416-445.
[6]	Kamla Kant MISHRA, Shruti DUBEY. APPROXIMATE CONTROLLABILITY OF NONLINEAR EVOLUTION FRACTIONAL CONTROL SYSTEM WITH DELAY[J]. 数学物理学报(英文版), 2025, 45(2): 553-568.
[7]	Lihua TAN, Yingzhe FAN. LOW-REGULARITY SOLUTIONS TO FOKKER-PLANCK-TYPE SYSTEMS IN THE WHOLE SPACE[J]. 数学物理学报(英文版), 2024, 44(6): 2361-2390.
[8]	Lin ZHENG, Shu WANG. THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME^*[J]. 数学物理学报(英文版), 2024, 44(5): 1877-1885.
[9]	Hao WANG. GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION[J]. 数学物理学报(英文版), 2024, 44(4): 1347-1372.
[10]	Weiyuan Zou. THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES QUATIONS IN THE WHOLE DOMAIN[J]. 数学物理学报(英文版), 2024, 44(3): 887-908.
[11]	Chenghua GAO, Xingyue HE, Jingjing WANG. THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM^*[J]. 数学物理学报(英文版), 2023, 43(6): 2615-2628.
[12]	Yazhou CHEN, Hakho HONG, Xiaoding SHI. THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D^*[J]. 数学物理学报(英文版), 2023, 43(5): 2133-2158.
[13]	Leilei CUI, Jiaxing GUO, Gongbao LI. THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1131-1160.
[14]	Bo Chen, Zhengmao Chen, Junhui Xie. PROPERTIES OF SOLUTIONS TO A HARMONIC-MAPPING TYPE EQUATION WITH A DIRICHLET BOUNDARY CONDITION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1161-1174.
[15]	Xuemei Zhang, Shikun Kan. SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1175-1194.

A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

A NOTE ON LARGE TIME BEHAVIOUR OF SOLUTIONS FOR VISCOUS CAHN-HILLIARD EQUATION

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0