具有不一定递减核的线性粘弹性波动方程振动传递问题的一般衰减估计

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1428-1444.

具有不一定递减核的线性粘弹性波动方程振动传递问题的一般衰减估计

刘志卿¹(),方钟波^2,*()

¹ 青岛科技大学数理学院山东青岛 266061
² 中国海洋大学数学科学学院山东青岛 266100

收稿日期:2020-01-08 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 方钟波 E-mail:Lzhiqing1005@163.com;fangzb7777@hotmail.com
作者简介:刘志卿, E-mail: Lzhiqing1005@163.com
基金资助:
山东省自然科学基金(ZR2019MA072);中央高校基本科研基金(201964008)

General Decay for the Transmission Problem of Viscoelastic Waves with not Necessarily Decreasing Kernel

Zhiqing Liu¹(),Zhongbo Fang^2,*()

¹ School of Mathematics and Physics, Qingdao University of Science and Technology, Shandong Qingdao 266061
² School of Mathematical Sciences, Ocean University of China, Shandong Qingdao 266100

Received:2020-01-08 Online:2021-10-26 Published:2021-10-08
Contact: Zhongbo Fang E-mail:Lzhiqing1005@163.com;fangzb7777@hotmail.com
Supported by:
the NSF of Shandong Province(ZR2019MA072);the Fundamental Research Funds for the Central Universities(201964008)

摘要/Abstract

摘要：

该文考虑一类记忆核不一定递减的线性粘弹性波动方程振动传递问题的渐近行为.通过构造新的Lyapunov泛函，导出问题能量的一般衰减估计值.同时，举例说明主要结论中包括指数、代数及对数等一致衰减估计.

关键词: 振动传递问题, 不一定递减的记忆核, 一般衰减估计

Abstract:

In this paper, we are concerned with the asymptotic behavior for a transmission problem of viscoelastic waves with not necessarily decreasing kernel. We construct a new Lyapunov functional to derive the general decay estimate. Meanwhile, we present an example to illustrate that the decay rate we obtained includes exponential, algebraic and logarithmic decay etc.

Key words: Transmission problem, Not necessarily decreasing kernel, General decay

中图分类号:

O175

刘志卿,方钟波. 具有不一定递减核的线性粘弹性波动方程振动传递问题的一般衰减估计[J]. 数学物理学报, 2021, 41(5): 1428-1444.

Zhiqing Liu,Zhongbo Fang. General Decay for the Transmission Problem of Viscoelastic Waves with not Necessarily Decreasing Kernel[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1428-1444.

图/表 1

参考文献 13

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