Email this article The Cauchy problem for the wave equation on homogeneous trees
- Authors: Tsvetkova A.V.1, Shafarevich A.I.1,2,3,4
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Affiliations:
- Lomonosov Moscow State University
- Ishlinskii Institute for Problems in Mechanics
- Moscow Institute of Physics and Technology (State University)
- National Research Center “Kurchatov Institute,”
- Issue: Vol 100, No 5-6 (2016)
- Pages: 862-869
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/149903
- DOI: https://doi.org/10.1134/S0001434616110262
- ID: 149903
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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.
About the authors
A. V. Tsvetkova
Lomonosov Moscow State University
Author for correspondence.
Email: moskal_1@mail.ru
Russian Federation, Moscow
A. I. Shafarevich
Lomonosov Moscow State University; Ishlinskii Institute for Problems in Mechanics; Moscow Institute of Physics and Technology (State University); National Research Center “Kurchatov Institute,”
Email: moskal_1@mail.ru
Russian Federation, Moscow; Moscow; Dolgoprudnyi, Moscow Oblast; Moscow
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