带势和转动惯量项的阻尼波动方程的快速能量衰减
Fast energy decay for damped wave equations with a potential and rotational inertia terms
AI总结：
针对一维空间中缺乏 Hardy、Poincaré 不等式工具的困难，本文研究带势与转动惯量项的阻尼波动方程 Cauchy 问题，利用势项补偿不足，证明了解的快速能量衰减与 L^2 衰减。
摘要：
我们考虑带势和转动惯量项的阻尼波动方程。研究该模型在一维欧几里得空间中的 Cauchy 问题，并得到当时间趋于无穷时解本身的快速能量衰减和 L^2 衰减。由于我们是在一维空间中考虑此问题，没有诸如 Hardy 和/或 Poincaré 不等式之类的有用工具，这给推导解和能量的衰减性质带来了显著困难。势项将在弥补这些弱点方面发挥作用。
英文摘要：
We consider damped wave equations with a potential and rotational inertia terms. We study the Cauchy problem for this model in the one dimensional Euclidean space and we obtain fast energy decay and L^2-decay of the solution itself as time goes to infinity. Since we are considering this problem in the one dimensional space, we have no useful tools such as the Hardy and/or Poincaré inequalities. This causes significant difficulties to derive the decay property of the solution and the energy. A potential term will play a role for compensating these weak points.
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