具有惯性项的Cahn-Hilliard方程的拉回吸引子  

Pullback attractors for Cahn-Hilliard equation with inertial term

作　　者：姜金平[1] 张晓雨 王小霞[1] Jiang Jinping;Zhang Xiaoyu;Wang Xiaoxia(College of Mathematics & Computer Science, Yan′an University, Yan′an 716000, China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《黑龙江科技大学学报》2022年第2期251-255,262,共6页Journal of Heilongjiang University of Science And Technology

基　　金：陕西省自然科学基础研究计划项目(2018JM1042)。

摘　　要：为解决具有惯性项的Cahn-Hilliard方程拉回吸引子存在性问题,以方程的能量解和拉回吸收集为研究对象,采用Faedo-Galerkin法证明在N≤3时能量解的存在性,借助拉回吸引子存在性定理,应用收缩函数的方法得到了在满足一定条件时,具有惯性项的Cahn-Hilliard方程拉回吸收集的渐近紧性。研究表明,在方程解存在且唯一的情况下,可通过拉回吸收集的渐近紧性得到方程拉回吸引子的存在性。This paper is aimed at solving the existence problem about the Cahn-Hilliard equation pullback attractors with inertial term.The description involves using the Faeto-Galerkin method to prove the existence of the energy solution as N≤3 by taking the energy solution and the pullback absorption set as the research object.Based on the theorem of existence of the pullback attractors,the asymptotic compactness of the pullback absorption set of the Cahn-Hilliard equation with inertial term is obtained by using the method of contraction function under certain conditions.It is shown that the existence of the pullback attractors of the equation can be obtained by using the asymptotic compactness of the pullback absorption set of the Cahn-Hilliard equation under the condition of unique equation solution.

关 键 词：CAHN-HILLIARD方程 惯性项 收缩函数 拉回吸引子 

分 类 号：O175.29[理学—数学]