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Infinite Propagation Speed For Wave Solutions on Some P.C.F. Fractals
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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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Cited by 1 Pith paper
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The existence of the solution of the wave equation on graphs
The wave equation on a finite weighted graph does have a unique solution, but the paper's explicit solution formula is wrong and its infinite propagation speed theorem rests on an impossible eigenfunction assumption.
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