线性耗散板方程解的衰减估计

doi:10.3969/j.cnki.jdxb.2017.06.003

吉首大学学报（自然科学版）

线性耗散板方程解的衰减估计

葛贝贝，刘永琴

（华北电力大学数理学院，北京 102206）

出版日期:2017-11-25 发布日期:2017-12-29
作者简介:葛贝贝（1990—），女，河北邯郸人，华北电力大学数理学院硕士研究生，主要从事偏微分方程研究；刘永琴（1979—），女，河南新乡人，华北电力大学数理学院副教授，主要从事偏微分方程研究.
基金资助:
国家自然科学基金青年科学基金资助项目（11201144,11201142）；教育部留学回国人员科研启动基金资助项目（2013B010）；中央高校基本科研业务费专项资金资助项目（2014MS57，2014MS63）

Decay Estimates of Solutions to a Linear Dissipative Plate Equation

GE Beibei,LIU Yongqin

(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

Online:2017-11-25 Published:2017-12-29

摘要/Abstract

摘要：

研究了多维空间（n≥1）中线性板方程的初值问题.使用Fourier变换，得到基本解和相应的线性问题的解.对Fourier空间中线性问题的解作逐点估计,得到解算子的估计和性质,再结合能量方法，得到线性问题解的最优衰减估计.

关键词： 线性板方程, Fourier变换, 衰减估计, 能量估计

Abstract:

In this paper the initial value problem of the linear plate equation in multi-dimensions (n≥1) is studied.The fundamental solutions and thus the solution to the corresponding linear problem are obtained by using Fourier transform.Requesting for the point-wise estimate of solution to the linear problem in the Fourier space,estimates and properties of solution operators are achieved,by utilizing which decay estimates of solutions to the linear problem are obtained.

Key words: linear plate equation, Fourier transform, decay estimates, energy estimates

葛贝贝，刘永琴. 线性耗散板方程解的衰减估计[J]. 吉首大学学报（自然科学版）, DOI: 10.3969/j.cnki.jdxb.2017.06.003.

GE Beibei,LIU Yongqin. Decay Estimates of Solutions to a Linear Dissipative Plate Equation[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2017.06.003.

参考文献

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线性耗散板方程解的衰减估计

Decay Estimates of Solutions to a Linear Dissipative Plate Equation

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