具衰退记忆的四阶拟抛物方程的长时间行为

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 114-124.

具衰退记忆的四阶拟抛物方程的长时间行为

彭小明¹,郑筱筱²,尚亚东^3,*()

¹ 广东财经大学统计与数学学院广州 510320
² 曲阜师范大学数学科学学院山东曲阜 273155
³ 广州大学数学与信息科学学院广州 510006

收稿日期:2017-06-30 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 尚亚东 E-mail:gzydshang@126.com

Global Attractors for a Fourth Order Pseudo-Parabolic Equation with Fading Memory

Xiaoming Peng¹,Xiaoxiao Zheng²,Yadong Shang^3,*()

¹ School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320
² School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273155
³ School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006

Received:2017-06-30 Online:2019-02-26 Published:2019-03-12
Contact: Yadong Shang E-mail:gzydshang@126.com

摘要/Abstract

摘要：

该文主要研究带衰退记忆和临界非线性的四阶拟抛物方程的长时间行为.在过去历史框架下，利用解算子半群的分解技巧和紧性转移定理证明了对应的动力系统的整体吸引子存在性.

关键词: 整体吸引子, 衰退记忆, 临界指数, 拟抛物

Abstract:

This paper is devoted to study the long-time dynamical behavior of fourth order pseudo-parabolic equations with memory when nonlinearity is critical. By using the decompose techniques of solution semigroup and compactness transitivity theorem, we show the existence of global attractors within the past history framework.

Key words: Global attractor, Fading memory, Critical exponent, Pseudo-parabolic

中图分类号:

O175.26

彭小明,郑筱筱,尚亚东. 具衰退记忆的四阶拟抛物方程的长时间行为[J]. 数学物理学报, 2019, 39(1): 114-124.

Xiaoming Peng,Xiaoxiao Zheng,Yadong Shang. Global Attractors for a Fourth Order Pseudo-Parabolic Equation with Fading Memory[J]. Acta mathematica scientia,Series A, 2019, 39(1): 114-124.

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