From resolvent estimates to damped waves
From resolvent estimates to damped waves
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DOI：
10.1007/s11854-014-0006-9
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
H. Christianson;E. Schenck;A. Vasy;J. Wunsch
中科院分区：
文献类型：
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作者：
H. Christianson;E. Schenck;A. Vasy;J. Wunsch
在这篇文章中，我们展示了如何获得衰减估计的阻尼波方程在一个紧凑的流形上没有几何控制通过知识的动力学附近的无阻尼集。我们表明，如果取代阻尼项与高阶复吸收potentialgives运营商享有多项式预解式界上的真实的轴，然后“预解式”相关的阻尼问题享有相同的顺序的界限。已知复吸收势的必要估计也可以由相应的非紧模型的估计通过胶合得到。
In this paper, we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the undamped set. We show that if replacing the damping term with a higher-ordercomplex absorbing potentialgives an operator enjoying polynomial resolvent bounds on the real axis, then the “resolvent” associated to our damped problem enjoys bounds of the same order. It is known that the necessary estimates with complex absorbing potential can also be obtained via gluing from estimates for corresponding non-compact models.