Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential 被引量：1

Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential

下载PDF

导出

摘要 In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential. In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.

作者 HUANG RUI YIN JING-XUE WANG LIANG-WEI

机构地区 School of Mathematical Sciences Institute of Mathematics

出处《Communications in Mathematical Research》 CSCD 2011年第2期156-168,共13页 数学研究通讯（英文版）

基金 The NSF(11001103) the SRFDP(200801831002) of China

关键词 Cahn-Hilliard equation concentration dependent mobility gradient de- pendent potential Cahn-Hilliard equation, concentration dependent mobility, gradient de- pendent potential

分类号 O152.1 [理学—基础数学] TK124 [动力工程及工程热物理—工程热物理]

引文网络
相关文献

参考文献2

1Yin Jingxue Huang Rui.A CAHN-HILLIARD TYPE EQUATION WITH GRADIENT DEPENDENT POTENTIAL[J].Journal of Partial Differential Equations,2008,21(1):77-96. 被引量：4
2Chang Chun LIU,Yuan Wei QI,Jing Xue YIN.Regularity of Solutions of the Cahn-Hilliard Equation with Non-constant Mobility[J].Acta Mathematica Sinica,English Series,2006,22(4):1139-1150. 被引量：3

二级参考文献23

1Novick-Cohen, A., Segel, L. A.: Nonlinear aspects of the Cahn--Hilliard equation. Physica D, 10, 277-298(1984)
2Cohen, D. S., Murrey, J. D.: A generalized diffusion model for growth and dispersal in a population. J.Math. Biology, 12, 237-249 (1981)
3Pego, R. L.: Front migration in the nonlinear Cahn-Hilliard equation. Proc. R. Soc. Lond., A, 422,261-278 (1989)
4Taylor, A. B.: Mathematical Models in Applied Mechanics, Clarendon, Oxford, 1986
5Zheng, S. M.: Mathematical results on the coupled Cahn-Hilliard equations, Proceedings of the Conference on Nonlinear Evolution Equations and Infinite-dimensional Dynamical Systems (Shanghai, 1995), 259-265,World Sci. Publishing, River Edge, N J, 1997
6Elliott, C. M., Zheng. S. M.: Onthe Cahn-Hilliard equation. Arch. Rat. Mech. Anal., 96, 339-357 (1986)
7Novick-Cohen, A.: On Cahn-Hilliard type equations. Nonlinear Analysis. TMA, 15, 797-814 (1990)
8Chen, X.: Global asymptotic limit of solutions of the Cahn-Hilliard equation. J. Differential Geom., 44,262-311 (1996)
9Alikakos, N. D., Bates, P. W., Chen, X. F.: Asymptotics of tile Cahn-Hilliard flow, Curvature flows and related topics (Levico, 1994), 13-23, GAKUTO Internat. Ser. Math. Sci. Appl., 1, Gakkotosho, Tokyo,1995
10Bernis, F., Friedman, A.: Higher order nonlinear degenerate parabolic equations. Journal of Differential Equations, 83, 179-206 (1990)

共引文献4

1柴世民,尹云光,宫成春,尹丽.一类Cahn-Hilliard方程弱解的存在惟一性[J].吉林大学学报（理学版）,2008,46(3):453-456. 被引量：1
2徐辽沙,黄锐,高天玲.具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程[J].吉林大学学报（理学版）,2009,47(6):1140-1144.
3Rui HUANG,Yang CAO.3-Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential[J].Journal of Mathematical Research and Exposition,2011,31(3):402-410.
4WANG Ling-Jun.Well-posedness for the Cahn-Hilliard Equation with Neumann Boundary Condition on the Half Space[J].Journal of Partial Differential Equations,2017,30(4):344-380.

同被引文献1

1Yin Jingxue Huang Rui.A CAHN-HILLIARD TYPE EQUATION WITH GRADIENT DEPENDENT POTENTIAL[J].Journal of Partial Differential Equations,2008,21(1):77-96. 被引量：4

引证文献1

1Rui HUANG,Yang CAO.3-Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential[J].Journal of Mathematical Research and Exposition,2011,31(3):402-410.

1Gary A．Sod,论立勇.流体动力学的数值方法初值与初边值问题[J].国外科技新书评介,2010(11):10-11.
2Rui HUANG,Yang CAO.3-Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential[J].Journal of Mathematical Research and Exposition,2011,31(3):402-410.
3Guo Jin-yong,Gao Wen-jie.Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation[J].Communications in Mathematical Research,2013,29(3):261-270.
4YING LungAn.Initial-boundary value problem of three phase flow in porous media[J].Science China Mathematics,2013,56(12):2799-2807.
5LU BO-QIANG,LI FENG-QUAN.The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations[J].Communications in Mathematical Research,2012,28(1):75-90.
6朱志平,杨广武.抛物型复方程初始边界值问题的稳定性(英文)[J].宁夏大学学报（自然科学版）,2000,21(1):13-16.
7曹春燕.Tb^(3+) concentration dependent optical properties and energy transfer in GdF_3 nanocrystals[J].Journal of Rare Earths,2013,31(11):1069-1073. 被引量：3
8游淑军,郭柏灵,宁效琦.INITIAL BOUNDARY VALUE PROBLEM FOR MODIFIED ZAKHAROV EQUATIONS[J].Acta Mathematica Scientia,2012,32(4):1455-1466. 被引量：1
9BAHSHELI Guliyev,AKBAR Barati Chiyaneh,NOVRUZ Bashirov,GENBER Kerimli.Effects of Nonparabolicity on Electron Thermopower of Size-Quantized Semiconductor Films[J].Chinese Physics Letters,2015,32(7):151-155.
10郭斌,高文杰.EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF NONLINEARITY[J].Acta Mathematica Scientia,2012,32(3):1053-1062. 被引量：3

Communications in Mathematical Research

2011年第2期

浏览历史

内容加载中请稍等...