具有Ventcel边界条件的波动方程解的长时间行为
Longtime behavior of the wave equations with Ventcel′s boundary conditions

本文对具有Ventcel边界条件和内部阻尼的波动方程解的长时间行为进行了研究. 为此, 本文首先建立了一类具有Ventcel边界条件的插值不等式; 然后由插值不等式出发得到了波动方程的预解式估计; 最后根据预解式估计得出了方程解的对数衰减结果.
This paper is devoted to study the longtime behavior of the solutions to the wave equations with boundary conditions, with an arbitrary small internal damping. For this purpose, we first establish an interpolation inequality with Ventcel′s boundary conditions. Then we obtain the resolvent estimate of the wave equation from the interpolation inequality. Finally, the resolvent estimate of the wave equation yields the logarithmic decay results