圆柱形波导中边界阻尼波的多项式急剧衰减

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-04-03 DOI:10.4310/mrl.2023.v30.n4.a10

Ruoyu P. T. Wang

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引用次数: 0

摘要

我们研究了在星形截面的紧凑和非紧凑波导的$C^{1,1}$边界上放置霍尔德连续阻尼的波方程的全局能量衰减。我们的研究表明，在违反几何控制条件的积圆柱的圆柱壁上，当阻尼自下而上均匀受限时，会出现尖锐的 $t^{-1/2}$ 衰减。在非积圆柱体上，我们还证明了当圆柱壁上的阻尼从下往上均匀受限时，会出现 $t^{-1/3}$ 衰减。

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Sharp polynomial decay for waves damped from the boundary in cylindrical waveguides

We study the decay of global energy for the wave equation with Hölder continuous damping placed on the $C^{1,1}$-boundary of compact and non-compact waveguides with star-shaped cross-sections. We show there is sharp $t^{-1/2}$-decay when the damping is uniformly bounded from below on the cylindrical wall of product cylinders where the Geometric Control Condition is violated. On non-product cylinders, we also show that there is $t^{-1/3}$-decay when the damping is uniformly bounded from below on the cylindrical wall.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.