| 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] |
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| 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 2256 全文点击 763 投稿时间：2019-06-28 修订日期：2019-09-05 |
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| 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 |
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| 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. |