Finer and Sharper Energy Decay Rate for an Elastic String with Localized Kelvin-Voigt Damping

发布时间:2018-05-15发布部门:非线性科学研究所

主题:   Finer and Sharper Energy Decay Rate for an Elastic String with Localized Kelvin-Voigt Damping主讲人:   刘壮一地点:   松江校区2号学院楼331理学院报告厅时间:   2018-05-18 15:00:00组织单位:   非线性科学研究所

主讲人简介:

1989 Ph.D, Mathematics, Virginia Polytechnic Institute and State University;1986 M.S., Mathematics, Virginia Polytechnic Institute and State University;1982 B.S., Mathematics, Fudan University, Shanghai, China;2012- Member of Advisory Board, China Center of the University of Minnesota;2009-2016 Head of Department of Mathematics and Statistics, University of Minnesota at Duluth;2000- present: Professor of Mathematics, University of Minnesota at Duluth.;1995-2000: Associate Professor of Mathematics, University of Minnesota at Duluth;1989-1995: Assistant Professor of Mathematics, University of Minnesota at Duluth.

Recipient of the 2011 University of Minnesota Award for Global Engagementand the title of Distinguished International Professor.

Recipient of the 2014 Dennis and Sabra Anderson Teaching and ScholarAward, Swenson College of Science Engineering, University of Minnesota Duluth.

Recipient of the 2017 Outstanding Graduate Advisor Award, Universityof Minnesota Duluth.

One monograph and over 60 papers.

内容摘要:

This talkis on the asymptotic behavior of the elastic string equation with localized Kelvin-Voigt damping

$$u_{tt}(x,t)-[u_{x}(x,t)+b(x)u_{x,t}(x,t)]_{x}=0,\; x\in(-1,1),\; t>0,$$

where $b(x)=0$ on $x\in (-1,0]$, and$b(x)=a(x)>0$ on $x\in (0,1)$.

Under the assumption that $a'(x)$ hasa singularity at $x=0$, we investigate the decay rate of the solution which depends on the order of the singularity.

When $a(x)$ behaves like $x^\a(-\logx)^{-\beta}$ near $x=0$ for $0\le\a<1, \;0\le\beta$ or $0<\a<1, \;\beta<0$,we show that the system can achieve a mixed polynomial-logarithmic decay rate.

As a byproduct, when $\beta=0$, weobtain the decay rate

$t^{-\frac{2-\a}{1-\a}}$ whichimproves the rate $t^{-\frac{1}{1-\a}}$ obtained in \cite{LZ}. The new rate isconsistent with the optimal decay rate $t^{-2}$ in the limit case $\a=0$ and$a(x)$ is a constant \cite{ARSVG}.

讲座主持:秦玉明 教授

讲座语言:英语

视频:   摄影: 撰写:秦玉明  信息员:唐晓亮  编辑:孙庆华

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