Abstract
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by analytical methods.
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Acknowledgments
Research supported in part by the NSF Grants DMS-1106982 and DMS-1262929. The authors are very grateful to Daniel Kelleher, Hugo Panzo and Antoni Brzoska for many helpful discussions, and to Luke Rogers for explaining the eigenfunction estimates based on his paper [51]. A.T. also thanks Sze-Man Ngai and Alexander Grigor’yan for very valuable advice. The authors thank anonymous referees for corrections and a substantial list of constructive suggestions leading to improvements in the first version of our paper, and for the suggestion to include the infinite wave propagation speed Remark 1.1.
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Communicated by Robert S. Strichartz.
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Andrews, U., Bonik, G., Chen, J.P. et al. Wave Equation on One-Dimensional Fractals with Spectral Decimation and the Complex Dynamics of Polynomials. J Fourier Anal Appl 23, 994–1027 (2017). https://doi.org/10.1007/s00041-016-9494-6
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DOI: https://doi.org/10.1007/s00041-016-9494-6