关于紧致黎曼流形上阻尼波和Schrödinger方程对数衰减的注记

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2023-02-09 DOI:10.4171/pm/2107

Iván Moyano, N. Burq

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引用次数: 1

摘要

在阻尼函数a=a（x）的作用下，我们考虑了类C1$cap$W2，$infty$的紧致黎曼流形（M，g）和M上的阻尼波或Schr“odinger方程。

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A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold

In this paper we consider a compact Riemannian manifold (M, g) of class C 1 $\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , under the action of a damping function a = a(x). We establish the following fact: if the measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then the decay in time of the associated energy is at least logarithmic.

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.