带有增值项的Cahn-Hilliard方程的全局吸引子
Global Attractor for the Cahn-Hilliard Equation with a Proliferation Term
DOI: 10.12677/AAM.2020.95092, PDF,   
作者: 任运平, 蒲志林, 段 芳：四川师范大学数学科学学院，四川 成都
关键词: 半群；全局吸引子；Cahn-Hilliard方程；Semigroup； Global Attractor； Cahn-Hilliard Equations
摘要: 本文研究带有增值项的Cahn-Hilliard方程在Hk空间上的全局吸引子的存在性问题。主要借助[8]中的方法，利用迭代过程和正则性估计，得到了全局吸引子的存在性结果。
Abstract: This paper is concerned with the existence of the global attractor of the Cahn-Hilliard equation with a proliferation term in Hk spaces. By means of the method in [8], the result of existence of global attractor is obtained by applying the iteration procedure and regularity estimates.
文章引用：任运平, 蒲志林, 段芳. 带有增值项的Cahn-Hilliard方程的全局吸引子[J]. 应用数学进展, 2020, 9(5): 772-781. https://doi.org/10.12677/AAM.2020.95092

参考文献

[1] Cahn, J.W. and Hilliard, J.E. (1958) Free Energy of a Nonuniform System: Interfacial Energy. The Journal of Chemical Physics, 28, 258-267. [Google Scholar] [CrossRef] 
[2] Novick-Cohen, A. and Segel, L.A. (1984) Nonlinear Aspects of the Cahn-Hilliard Equation. Physica D: Nonlinear Phenomena, 10, 277-298. [Google Scholar] [CrossRef] 
[3] Nicolaenko, B., Scheurer, B. and Temam, R. (1989) Some Global Dynamical Properties of a Class of Pattern Formation Equations. Communications in Partial Differential Equations, 14, 245-297. [Google Scholar] [CrossRef] 
[4] Temam, R. (1997) Infinite-Dimensional Dynamical Systems in Mechanics and Physics. 2nd Edition, Applied Mathematical Sciences, Vol. 68, Springer-Verlag, New York.
[5] Cholewa, J.W. and Dlotko, T. (1994) Global Attractor for the Cahn-Hilliard System. Bulletin of the Australian Mathematical Society, 49, 277-292. [Google Scholar] [CrossRef] 
[6] Dlotko, T. (1994) Global Attractor for the Cahn-Hilliard Equation in H2 and H3. Journal of Differential Equations, 113, 381-393. [Google Scholar] [CrossRef] 
[7] Li, D. and Zhong, C.K. (1998) Global Attractor for the Cahn-Hilliard System with Fast Growing Nonlinearity. Journal of Differential Equations, 149, 191-210. [Google Scholar] [CrossRef] 
[8] Song, L., Zhang, Y. and Ma, T. (2009) Global Attractor of the Cahn-Hilliard Equation in Hk Spaces. Journal of Mathematical Analysis Applications, 355, 53-62. [Google Scholar] [CrossRef] 
[9] Miranville, A. (2013) Asymptotic Behaviour of a Generalized Cahn-Hilliard Equation with a Proliferation Term. Applicable Analysis, 92, 1308-1321. [Google Scholar] [CrossRef] 
[10] Miranville, A. (2019) Existence of Solutions to a Cahn-Hilliard Type Equation with a Logarithmic Nonlinear Term. Mediterranean Journal of Mathematics, 16, Article No. 6. [Google Scholar] [CrossRef] 
[11] Miranville, A. (2011) Asymptotic Behavior of the Cahn-Hilliard-Oono Equation. Journal of Applied Analysis and Computation, 1, 523-536.
[12] Khain, E. and Sander, L.M. (2008) A Generalized Cahn-Hilliard Equation for Biological Applications. Physical Review E, 77, Article ID: 051129. [Google Scholar] [CrossRef] 
[13] Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, Vol. 44, Springer-Verlag, Berlin. [Google Scholar] [CrossRef] 

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