The Green function for waves on the $2$-regular Bethe lattice
Analysis of PDEs
2017-11-07 v1
Abstract
In this paper, we compute an explicit analytic expression for the Green function of the wave operator on the -regular lattice called the "Bethe lattice" equipped with its standard metric. In particular, we exhibit a phenomena of abnormal speed of propagation for waves: the effective speed of propagation of energy for large time is , and there exists a true propagation at any speed .
Cite
@article{arxiv.1711.01363,
title = {The Green function for waves on the $2$-regular Bethe lattice},
author = {Kaïs Ammari and Gilles Lebeau},
journal= {arXiv preprint arXiv:1711.01363},
year = {2017}
}