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

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。
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