粘性Cahn-Hilliard方程的整体吸引子
Global Attractor for the Viscous Cahn-Hilliard Equation
DOI: 10.12677/AAM.2016.54094, PDF, HTML, XML, 下载: 1,554  浏览: 3,723  科研立项经费支持
作者: 任永华：太原理工大学数学学院，山西 太原
关键词: 粘性Cahn-Hilliard方程；整体吸引子；吸收集；Viscous Cahn-Hilliard Equation； Global Attractor； Absorbing Set
摘要: 本文研究了带有非线性项的粘性Cahn-Hilliard方程的整体吸引子。首先验证了该方程有界吸收集的存在性，进而利用紧性方法得到整体吸引子的存在性。
Abstract: We consider the global attractor of the viscous Cahn-Hilliard equation with a nonlinear term. Firstly, it proved the existence of bounded absorbing set, then obtained the existence of global attractor by a new method of obtaining the compactness.
文章引用：任永华. 粘性Cahn-Hilliard方程的整体吸引子[J]. 应用数学进展, 2016, 5(4): 818-822. http://dx.doi.org/10.12677/AAM.2016.54094

参考文献

[1] 董超雨, 姜金平, 张晓明. 粘性Cahn-Hilliard方程全局吸引子的存在性[J]. 湖北大学学报, 2014, 36(4): 385-388.
[2] 黄青霞, 李扬荣, 曾雪萍. 带有可加白噪音的Cahn-Hilliard方程的吸引子[J]. 西南大学学报, 2007, 29(11): 1-6.
[3] 何春燕, 张法勇. Cahn-Hilliard方程的拟谱逼近的长时间性态[J]. 黑龙江大学自然科学学报, 2006, 23(6): 779- 786.
[4] 刘转玲. 一类非经典扩散方程在强拓扑空间中的指数吸引子[J]. 应用泛函分析学报, 2013, 15(3): 287-290.
[5] Yang, Z.J. (2009) Global Attractor for a Nonlinear Wave Equation Arising in Elastic Waveguide Model. Nonlinear Analysis: Theory, Methods & Applications, 70, 2132-2142.
https://doi.org/10.1016/j.na.2008.02.114
[6] 茶丽芳, 林国广. 耗散Camassa-Holm方程的整体吸引子[J]. 云南大学学报, 2009, 31(S2): 348-353.
[7] Yang, Z.J. and Li, X. (2011) Finite-Dimensional Attractors for the Kirchhoff Equation with a Strong Dissipation. Journal of Mathematical Analysis and Applications, 375, 579-593.
https://doi.org/10.1016/j.jmaa.2010.09.051
[8] Yang, Z.J. (2011) A Global Attractor for the Elastic Waveguide Model. Nonlinear Analysis: Theory, Methods & Applications, 74, 6640-6661.
https://doi.org/10.1016/j.na.2011.06.045
[9] Ma, Q.F., Wang, S.H. and Zhong, C.K. (2002) Necessary and Sufficient Conditions for the Existence of Global Attractors for Semigroup and Application. Indiana University Mathematics Journal, 51, 1541-1559.
https://doi.org/10.1512/iumj.2002.51.2255

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