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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
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.
Received: 01.06.2016
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
Linking options:
https://www.mathnet.ru/eng/mzm11410https://doi.org/10.4213/mzm11410 https://www.mathnet.ru/eng/mzm/v100/i6/p923
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Abstract page: | 457 | Full-text PDF : | 102 | References: | 61 | First page: | 26 |
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