Infinite Propagation Speed For Wave Solutions on Some P.C.F. Fractals

2011/11/12 by Yin-Tat Lee, Lee, Yin-Tat
Mathematics · #28A80 #35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:28A80 #msc:35L05

paper · pdf · doi:10.48550/arxiv.1111.2938

Version 3: Some mistakes in section 6 are fixed

arxiv created 2012/10/01 · arxiv updated 2012/10/02

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.

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