Non uniform decay of the total energy of the dissipative wave equation
Non uniform decay of the total energy of the dissipative wave equation
复制标题
耗散波方程总能量的非均匀衰减
DOI：
10.18910/12375
复制
发表时间：
2009
影响因子：
0.4
通讯作者：
H. Nishiyama
中科院分区：
文献类型：
--
作者：
H. Nishiyama
Kawashita、Nakazawa 和 Soga [3] 给出了主项具有常数系数的耗散波动方程能量均匀衰减的必要条件。在他们的证明中，他们为合适的柯西数据族构建了渐近解。在本文中，我们考虑与族相关的半经典测度，而不是渐近解，并将这一结果扩展到可变系数的情况。此外，我们给出了能量衰减的一些下限估计。
Kawashita, Nakazawa, and Soga [3] give a necessary condition for the uniform energy decay of the dissipative wave equation whose principal term has constant coefficients. In their proof, they construct asymptotic solutions for a suitable family of the Cauchy data. In this paper, instead of the asymptotic solutions, we consider the semiclassical measure associated with the family and extend this result to the variable coefficient case. Moreover we give some lower bound estimate for the energy decay.