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Matematicheskie Zametki, 2016, Volume 100, Issue 6, Pages 923–931
DOI: https://doi.org/10.4213/mzm11410 (Mi mzm11410) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Cauchy Problem for the Wave Equation on Homogeneous Trees

A. V. Tsvetkovaa, A. I. Shafarevichabcd

a Lomonosov Moscow State University
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
d National Research Centre "Kurchatov Institute", Moscow
Full-text PDF (458 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm11410
Abstract: The wave equation on an infinite homogeneous tree is studied. For the Laplace operator, the Kirchhoff conditions are taken as the matching conditions at the vertices. A solution of the Cauchy problem is obtained and the behavior of the wave energy as time tends to infinity is described. It is shown that part of the energy does not go to infinity, but remains on the edges of the trees. The part of the energy remaining on the edges depends on the branching number.
Keywords: wave equation on a graph, distribution of energy, spectrum of the second derivative operator on a homogeneous tree.
Funding agency Grant number
Russian Science Foundation 16-11-10069
This work was supported by the Russian Science Foundation under grant 16-11-10069.
Received: 01.06.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 6, Pages 862–869
DOI: https://doi.org/10.1134/S0001434616110262
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. V. Tsvetkova, A. I. Shafarevich, “The Cauchy Problem for the Wave Equation on Homogeneous Trees”, Mat. Zametki, 100:6 (2016), 923–931; Math. Notes, 100:6 (2016), 862–869
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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