Rn空间中带有密度函数的四阶粘弹方程的一致衰减性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 122-133.

Rⁿ空间中带有密度函数的四阶粘弹方程的一致衰减性

冯保伟¹, 苏克勤²

1. 西南财经大学经济数学学院成都 611130;
2. 河南农业大学信息与管理科学学院郑州 450046

收稿日期:2016-10-28 修回日期:2017-04-01 出版日期:2018-02-26 发布日期:2018-02-26
通讯作者: 冯保伟 E-mail:bwfeng@swufe.edu.cn
作者简介:苏克勤,keqinsu@hotmail.com
基金资助:
国家自然科学基金（11701465），中内高校基本科研业务费（JBK170127）和河南省高等学校重点科研项目（16A110032）

Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rⁿ

Feng Baowei¹, Su Keqin²

1. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130;
2. College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046

Received:2016-10-28 Revised:2017-04-01 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11701465), the Fundamental Research Funds for the Central Universities (JBK170127) and the Key University Science Research Project of Henan Province (16A110032)

摘要/Abstract

摘要： 该文研究了一个Rⁿ（n≥4）空间中带有密度函数的四阶粘弹方程.为了弥补Poincaré不等式在Rⁿ空间中的不足，作者引入了一个加权空间.在对松弛函数适当的假设下，作者利用能量扰动的方法建立了初边值问题解的一致衰减性结果，并且该结果推广了前人的结果.

关键词: 能量衰减, 四阶方程, 加权空间, 密度

Abstract: In this paper, we investigate a fourth-order linear viscoelastic equation with density in the whole space Rⁿ (n ≥ 4). To compensate the lack of Poincaré's inequality in Rⁿ, we consider the solutions in weighted spaces. Under suitable assumptions on the relaxation function, we establish a general decay result of solution for the initial value problem by using energy perturbation method. Our result extends earlier results.

Key words: Energy decay, Fourth-order equation, Weighted space, Density

中图分类号:

O175.21

冯保伟, 苏克勤. Rⁿ空间中带有密度函数的四阶粘弹方程的一致衰减性[J]. 数学物理学报, 2018, 38(1): 122-133.

Feng Baowei, Su Keqin. Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rⁿ[J]. Acta mathematica scientia,Series A, 2018, 38(1): 122-133.

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Rⁿ空间中带有密度函数的四阶粘弹方程的一致衰减性

Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rⁿ

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