阻尼wave equations的本征频率和展开式
Eigenfrequencies and expansions for damped wave equations
摘要：
研究了紧致流形上阻尼波方程的本征频率和传播子展开式。在几何控制的假设下，传播子被证明在实轴附近允许一个多本征模的扩展，误差项随时间呈指数衰减。在非退化椭圆闭测地线不满足阻尼系数支撑的情况下，我们证明了存在一个快速收敛到实轴的本征频率序列。在Zoll流形的情况下，我们表明，传播子可以扩展在集群的本征频率在整个谱带。
英文摘要：
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, the propagator is shown to admit an expansion in terms of finitely many eigenmodes near the real axis, with an error term exponentially decaying in time. In the presence of a nondegenerate elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds, we show that the propagator can be expanded in terms of clusters of the eigenfrequencies in the entire spectral band.
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