板方程和波方程所构成的传输方程主要应用于噪音控制的研究。目前在此类方程的研究中，为了使整个传输方程稳定，多见于在板和波上都施加阻尼(直接阻尼)，然而只在板/波上施加局部阻尼(间接阻尼)的研究还很少。相对于在整个方程上施加阻尼而言，施加在局部的阻尼更易实现，因此更具有研究价值且所需要的数学工具更为复杂。 . 本项目拟对一类带有局部间接阻尼的板-波传输方程的稳定性问题开展研究，基于频域分析法和能量乘子技巧进行其方程能量的衰减估计。从控制的角度来看，该传输方程所描述的物理模型可看作是由被控对象和动态反馈控制器耦合而成的闭环系统。本项目只利用板/波的局部阻尼去镇定整个传输方程，以及阐明此类传输方程能量的衰减率依赖于其间接阻尼的类型、阻尼的区域和方程所在的区域是否满足几何控制条件等诸多因素。预期研究成果不仅可以丰富耦合分布参数系统的数学控制理论，也可以为相关工程技术问题提供理论指导。

The transmission equation composed of plate equation and wave equation is widely used in the study of noise control. Most of the studies focus on the damping distributes in plate equation and the wave equation (direct damping). However, there is a few of study on stabilization of the whole equation with local damping of palte/wave (indirect damping). Compared with the global damping, the local damping is more easily achieved and demands more sophisticated mathematical instruments. . This project considers the stability of the transmission plate-wave equations with local indirect damping. By using the frequency domain approach and multiplier technique, the energy decay rates for the whole transmission equation are obtained. From the control perspective, the transmission equation consists of the dynamic control and original system. The purpose of this project is to stabilize the whole transmission equation by the local damping of wave/plate, and to clarify that the stability of such transmission equation depends on many factors, such as the type of indirect damping, damping locations, and whether domain of equation fulfills some special geometric conditions. The research can not only enrich the mathematical control theory of coupled distributed parameter system, but also provide theoretical guidance for related engineering technical problems.