Infinite Propagation Speed For Wave Solutions on Some P.C.F. Fractals
Analysis of PDEs
2012-10-02 v3
Abstract
From the finite difference method for wave equation on p.c.f. fractals, we would expect that infinite prorogation speed property for wave solutions on a large class of p.c.f. fractals. We prove that is true if the heat kernel satisfies the sub-Gaussian lower bound. Furthermore, we provide a sub-Gaussian upper bound for wave kernel given the heat kernel sub-Gaussian upper bound.
Cite
@article{arxiv.1111.2938,
title = {Infinite Propagation Speed For Wave Solutions on Some P.C.F. Fractals},
author = {Yin-Tat Lee},
journal= {arXiv preprint arXiv:1111.2938},
year = {2012}
}
Comments
Version 3: Some mistakes in section 6 are fixed