高维环面上带粗糙阻尼的波动方程的稳定化
偏微分方程分析
2024-05-22 v4
摘要
本文研究阻尼波动方程的均匀稳定化。当流形紧致且阻尼连续时，几何控制条件已知为必要且充分。在二维环面上阻尼为多边形特征函数之和的情形，Burq-Gérard 的结果指出：稳定化发生当且仅当每条测地线都与阻尼区域内部相交或两侧擦过阻尼多边形。我们将其结果自然推广至任意维数 环面上的充分条件。在某些特定情形下，我们证明该充分条件可被弱化。
引用
@article{arxiv.2303.03733,
title = {Stabilization of the wave equation on larger-dimension tori with rough dampings},
author = {Marc Rouveyrol},
journal= {arXiv preprint arXiv:2303.03733},
year = {2024}
}
备注
32 pages, 7 figures. Accepted in Pure and Applied Analysis. Text overlap with arXiv:1801.00983 --- Updates in v2 : extended bibliography. Updates in v3 : explicit statement of the main result of Section 5 added (Theorem 5 of the introduction). Sections 1 and 5 modified accordingly. Corollary 2.2 made more precise. Other minor corrections. --- Updates in v4 : revisions based on referee remarks