一类四阶非线性发展方程的整体吸引子

一类四阶非线性发展方程的整体吸引子

Global Attractor for a Class of Fourth-Order Nonlinear Evolution Equations

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吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (4): 793-799.

杨佳雪, 段宁

东北大学理学院, 沈阳 110004

收稿日期:2021-11-05 出版日期:2022-07-26 发布日期:2022-07-26
通讯作者: 段宁 E-mail:duanning@mail.neu.edu.cn

YANG Jiaxue, DUAN Ning

College of Sciences, Northeastern University, Shenyang 110004, China

Received:2021-11-05 Online:2022-07-26 Published:2022-07-26

摘要： 利用解的先验估计和算子半群的渐近紧性, 考虑描述动力学控制晶体生长过程的四阶非线性发展方程的整体动力学行为, 证明当方程的初值属于H¹(0,1)时, 在H⁴(0,1)空间中方程整体吸引子的存在性.

关键词: 整体吸引子, 非线性发展方程, 整体弱解

Abstract: By using a priori estimates of the solution and the asymptotic compactness of the operator semigroup, we considered the global dynamic behavior of a fourth-order nonlinear evolution equation describing the dynamic controll of crystal growth process, and proved the existence of global attractor of the equation in H⁴(0,1) space when the initial value of the equation belonged to H¹(0,1).

Key words: global attractor, nonlinear evolution equation, global weak solution

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杨佳雪, 段宁. 一类四阶非线性发展方程的整体吸引子[J]. 吉林大学学报(理学版), 2022, 60(4): 793-799.

YANG Jiaxue, DUAN Ning. Global Attractor for a Class of Fourth-Order Nonlinear Evolution Equations[J]. Journal of Jilin University Science Edition, 2022, 60(4): 793-799.

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[1]	鲍茜, 段宁, 赵晓朋. 一类高阶扩散方程的整体吸引子[J]. 吉林大学学报(理学版), 2018, 56(2): 316-319.
[2]	常晶, 祝英杰, 高忆先, 赵昕. 一类五阶非线性发展方程的孤波解[J]. 吉林大学学报(理学版), 2015, 53(06): 1214-1216.