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

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

2011-11-12

arxiv.org/abs/1111.2938v2

Mathematics

Analysis of PDEs

18 pages, 4 figures Version 2: The homogeneous tree section have been removed. (It will be moved to another paper.) The wave k

Scientific paper

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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