积流形上的拉普拉斯特征函数与阻尼波动方程

Applied mathematics research express : AMRX Pub Date : 2015-03-18 DOI:10.1093/AMRX/ABV005

N. Burq, C. Zuily

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引用次数: 11

摘要

-本文的目的是研究拉普拉斯算子(或更一般的拟模)在积流形上的特征函数的可能集中。我们证明了第一作者和Zworski[10,11]的方法适用于(模还原)并推导出弱阻尼波动方程的新稳定结果，这些结果扩展到积流形，这是由Leautaud-Lerner[12]在环面积上得到的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Laplace Eigenfunctions and Damped Wave Equation on Product Manifolds

- The purpose of this article is to study possible concentrations of eigenfunc-tions of Laplace operators (or more generally quasi-modes) on product manifolds. We show that the approach of the first author and Zworski [10, 11] applies (modulo rescalling) and deduce new stabilization results for weakly damped wave equations which extend to product manifolds previous results by Leautaud-Lerner [12] obtained for products of tori.

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Applied mathematics research express : AMRX

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