Wave Propagation Speed on Fractals

Sze Man Ngai, Wei Tang, Yuanyuan Xie

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We study the wave propagation speed problem on metric measure spaces, emphasizing on self-similar sets that are not post-critically finite. We prove that a sub-Gaussian lower heat kernel estimate leads to infinite propagation speed, extending a result of Lee (Infinite propagation speed for wave solutions on some p.c.f. fractals, https://archive.org/details/arxiv-1111.2938) to include bounded and unbounded generalized Sierpiński carpets, some fractal blowups, and certain iterated function systems with overlaps. 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.

Original languageEnglish
Article number31
JournalJournal of Fourier Analysis and Applications
Volume26
Issue number2
DOIs
StatePublished - Apr 1 2020

Keywords

  • Bernoulli convolution
  • Fractal
  • Heat-kernel estimate
  • Laplacian
  • Wave propagation speed

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