引用本文:付晓玉,柳絮,朱先政.具Cauchy-Ventcel边界的阻尼波方程的对数衰减性(英文)[J].控制理论与应用,2019,36(11):1879~1885.[点击复制]
FU Xiao-yu,LIU Xu,ZHU Xian-zheng.Logarithmic decay of wave equations with Cauchy-Ventcel boundary conditions[J].Control Theory and Technology,2019,36(11):1879~1885.[点击复制]
具Cauchy-Ventcel边界的阻尼波方程的对数衰减性(英文)
Logarithmic decay of wave equations with Cauchy-Ventcel boundary conditions
摘要点击 2260  全文点击 763  投稿时间:2019-06-28  修订日期:2019-09-05
查看全文  查看/发表评论  下载PDF阅读器
DOI编号  10.7641/CTA.2019.90490
  2019,36(11):1879-1885
中文关键词  对数衰减  波方程  Cauchy-Ventel边界  Carleman估计
英文关键词  Logarithmic decay  wave equations  Cauchy-Ventcel boundary condition  Carleman estimate
基金项目  
作者单位E-mail
付晓玉 四川大学 xiaoyufu@scu.edu.cn 
柳絮 东北师范大学  
朱先政* 四川大学 sinchch@qq.com 
中文摘要
      本文研究有界区域上具Cauchy-Ventcel边界条件的波动方程的解的衰减性质。在不要求耗散区域满足几何控制条件的情形下,我们得到了波方程的对数衰减结果。 主要结果的证明依赖于具Cauchy-Ventcel边界条件的椭圆方程的插值不等式以及关于该椭圆方程的预解式估计。为得到期望的插值不等式, 我们采用的工具是整体Carleman估计。
英文摘要
      This paper is devoted to a study of decay properties for a class of wave equations with Cauchy-Ventcel boundary conditions and a local internal damping. Based on an estimate on the resolvent operator, solutions of the wave equations under consideration are proved to decay logarithmically without any geometric control condition. The proof of the decay result relies on the interpolation inequalities for an elliptic equation with Cauchy-Ventcel boundary conditions and the estimate of the resolvent operator for that equation. The main tool to derive the desired interpolation inequality is global Carleman estimate.