Spectral asymptotics for the vectorial damped wave equation

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-11-17 DOI:10.1080/03605302.2022.2137678

Guillaume Klein

引用次数: 0

Abstract

Abstract The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. Sjöstrand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.

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矢量阻尼波动方程的谱渐近性

摘要与标量阻尼波动方程相关的本征频率属于平行于实轴的频带。Sjöstrand表明，在密度为0的情况下，本征频率被限制在由阻尼项的Birkhoff极限确定的较薄频带中。在这篇文章中，我们证明了这个结果对于矢量阻尼波动方程仍然成立。在这个设置中，阻尼项给出的共循环的李雅普诺夫指数起到了标量设置的Birkhoff极限的作用。

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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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.