标题： 局部衰减和阻尼波动方程在渐近欧几里得情形下的渐近概貌 显示英文标题

标题： Local decay and asymptotic profile for the damped wave equation in the asymptotically Euclidean setting

摘要： 我们证明了在渐近欧几里得环境中波动方程的局部衰减估计。 在偶数维中，我们超越了最优衰减，提供了由自由波动方程解给出的大时间渐近轮廓。 在奇数维中，我们改进了已知的最佳估计。 特别是，我们得到了比偶数维中可能的最优衰减更好的衰减率。 分析主要依赖于对低频情况下相应预解算子与自由问题预解算子的比较。 此外，所有结果都适用于具有短程吸收指数的阻尼波动方程。 显示英文摘要

摘要： We prove local decay estimates for the wave equation in the asymptotically Euclidean setting. In even dimensions we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation. In odd dimensions, we improve the best known estimates. In particular, we get a decay rate that is better than what would be the optimal decay in even dimensions. The analysis mainly relies on a comparison of the corresponding resolvent with the resolvent of the free problem for low frequencies. Moreover, all the results hold for the damped wave equation with short range absorption index.