Wave propagation speed on fractals

Sze-Man Ngai Hunan Normal University and Georgia Southern University Wei Tang Hunan Normal University Yuanyuan Xie Hunan Normal University

Analysis of PDEs mathscidoc:1701.03001

We study the wave propagation speed problem on metric measure spaces, emphasizing on self-similar sets that are not postcritically finite. We prove that a sub-Gaussian lower heat kernel estimate leads to infinite propagation speed, extending a result of Y.-T. Lee to include bounded and unbounded generalized Sierpi\'nski carpets as well as some fractal blowups. We also formulate conditions under which a Gaussian upper heat kernel estimate leads to finite propagation speed, and apply this result to two classes of iterated function systems with overlaps, including those defining the classical infinite Bernoulli convolutions.
Wave propagation speed, fractal, Laplacian, heat-kernel estimate, Bernoulli convolution
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@inproceedings{sze-manwave,
  title={Wave propagation speed on fractals},
  author={Sze-Man Ngai, Wei Tang, and Yuanyuan Xie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170105180458514550707},
}
Sze-Man Ngai, Wei Tang, and Yuanyuan Xie. Wave propagation speed on fractals. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170105180458514550707.
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