线性波的浓度接近锥

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-09-17 DOI:10.4171/rmi/1399

R. Cote, C. Laurent

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引用次数: 10

摘要

我们关心的是线性波动方程的解。通过与Radon变换相关的算子，给出了在能量空间有效的大时间渐近公式。这使我们能够证明能量集中在光锥附近。这允许推导出外部能量的进一步表达式(在移位光锥之外)。我们特别推广了在径向环境下得到的[CKS14]公式。在奇维，我们研究了外部能量与初始能量的差异，并在一般情况下证明了[KLLS15]的结果(仅限于径向数据)。

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Concentration close to the cone for linear waves

We are concerned with solutions to the linear wave equation. We give an asymptotic formula for large time, valid in the energy space, via an operator related to the Radon transform. This allows us to show that the energy is concentrated near the light cone. This allows to derive further expressions the exterior energy (outside a shifted light cone). We in particular generalize the formulas of [CKS14] obtained in the radial setting. In odd dimension, we study the discrepancy of the exterior energy regarding initial energy, and prove in the general case the results of [KLLS15] (which were restricted to radial data).

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来源期刊

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.