In this paper, we consider Carleman estimates for the damped fourth-order plate operators ${\mathrm{\partial }}_{tt}-\rho {\mathrm{\partial }}_t\mathrm{\Delta }+{\mathrm{\Delta }}^2$ in a bounded smooth domain with Robin boundary conditions. Because the appearance of such kind of structural damping, the speed of propagation for solutions to the plate equation is infinite and the corresponding properties of the solution similar to heat equations, and is significantly different from that of the usual plate equations without damping. As applications, we consider two types of inverse problems in determining source terms for the plate equation with structural damping. The time-dependent measurements can be restricted to an arbitrary small sub-domain or arbitrary sub-boundary, respectively. Under some assumptions on the regularity of the solutions and coefficients, we prove the global stability results for these inverse problems.

在本文中，我们考虑了阻尼四阶板算子的 Carleman 估计${\mathrm{\partial }}_{吨吨}-\rho {\mathrm{\partial }}_{吨}\mathrm{\Delta }+{\mathrm{\Delta }}^2$在具有 Robin 边界条件的有界平滑域中。由于这种结构阻尼的出现，板方程解的传播速度是无限的，其解的相应性质类似于热方程，与通常没有阻尼的板方程有显着差异。作为应用，我们在确定具有结构阻尼的板方程的源项时考虑了两种类型的逆问题。与时间相关的测量可以分别限制在任意小的子域或任意子边界。在对解和系数的规律性的一些假设下，我们证明了这些逆问题的全局稳定性结果。