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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 265–275
DOI: https://doi.org/10.4213/tm4069 (Mi tm4069) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph

A. V. Tsvetkovaa, A. I. Shafarevichabcd

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
c National Research Center “Kurchatov Institute,” pl. Akademika Kurchatova 1, Moscow, 123182 Russia
d Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
Full-text PDF (223 kB) Citations (2)
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DOI: https://doi.org/10.4213/tm4069
Abstract: We consider a variable-velocity wave equation on the simplest decorated graph obtained by gluing a ray to the three-dimensional Euclidean space, with localized initial conditions on the ray. The wave operator should be self-adjoint, which implies some boundary conditions at the gluing point. We describe the leading part of the asymptotic solution of the problem using the construction of the Maslov canonical operator. The result is obtained for all possible boundary conditions at the gluing point.
Funding agency Grant number
Russian Science Foundation 16-11-10069
This work is supported by the Russian Science Foundation under grant 16-11-10069.
Received: October 27, 2019
Revised: November 6, 2019
Accepted: December 11, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 250–260
DOI: https://doi.org/10.1134/S0081543820010204
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. V. Tsvetkova, A. I. Shafarevich, “Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 265–275; Proc. Steklov Inst. Math., 308 (2020), 250–260
Citation in format AMSBIB
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\paper Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 308
\pages 265--275
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4069}
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  • https://doi.org/10.4213/tm4069
  • https://www.mathnet.ru/eng/tm/v308/p265
    • This publication is cited in the following 2 articles:
    1. A. V. Tsvetkova, A. I. Shafarevich, “The wave equation with symmetric velocity on the hybrid manifold obtained by gluing a ray to a three-dimensional sphere”, Trans. Moscow Math. Soc., 82 (2021), 305–325  mathnet  crossref
    2. A. V. Tsvetkova, A. I. Shafarevich, “Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph with Initial Conditions on a Surface”, Math. Notes, 108:4 (2020), 590–602  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Full-text PDF :73
    References:51
    First page:14
     
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