Asymptotic Boundary Observability For The Wave Equation On Simplices
Analysis of PDEs
2020-04-07 v1
Abstract
In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet boundary conditions. Our main result is an asymptotic observability identity from any one face of the simplex. The novel aspects of the result are that it is a large-time asymptotic rather than an estimate, and it requires no dynamical assumptions on the billiard flow. The proof uses mainly integrations by parts.
Cite
@article{arxiv.2004.01748,
title = {Asymptotic Boundary Observability For The Wave Equation On Simplices},
author = {Hans Christianson and Ziqing Lu},
journal= {arXiv preprint arXiv:2004.01748},
year = {2020}
}
Comments
15 pages, 3 figures