论文标题
时间依赖性阻尼波方程的能量衰减
Energy decay for the time dependent damped wave equation
论文作者
论文摘要
在紧凑的riemannian歧管上建立了阻尼波动方程的能量衰减，其中允许阻尼系数依赖时间。使用依赖时间的可观察性不平等，显示溶液的能量以指数速率衰减，如果阻尼系数满足经典几何控制条件的时间依赖性类似物。通过在允许的初始数据上删除技术假设，可以改善现有的依赖时间的可观察性不平等。
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions decays at an exponential rate if the damping coefficient satisfies a time dependent analogue of the classical geometric control condition. Existing time dependent observability inequalities are improved by removing technical assumptions on the permitted initial data.
