Concentration close to the cone for linear waves
Analysis of PDEs
2021-09-23 v2
Abstract
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).
Keywords
Cite
@article{arxiv.2109.08434,
title = {Concentration close to the cone for linear waves},
author = {Raphaël Côte and Camille Laurent},
journal= {arXiv preprint arXiv:2109.08434},
year = {2021}
}