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Localized asymptotic solutions of the wave equation with variable velocity on the simplest graphs

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Abstract

The asymptotic behavior of the Cauchy problem for the wave equation with variable velocity and localized initial conditions on the line, semi-axis, and an infinite starlike graph is described. The solution consists of a short-wave and long-wave parts; the shortwave part moves along the characteristics, while the long-wave part satisfies the Goursat or Darboux problem. In the case of a star-like graph, the distribution of energy with respect to the edges is discussed; this distribution depends on the arrangement of the eigensubspaces of the unitary matrix that defines the boundary condition at the vertex of the star.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, Russia

    A. I. Allilueva & A. I. Shafarevich

  2. M. V. Lomonosov Moscow State University, Moscow, Russia

    A. I. Shafarevich

  3. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  4. National Research Centre “Kurchatov Institute”, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

Authors
  1. A. I. Allilueva
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  2. A. I. Shafarevich
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Correspondence to A. I. Allilueva.

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Allilueva, A.I., Shafarevich, A.I. Localized asymptotic solutions of the wave equation with variable velocity on the simplest graphs. Russ. J. Math. Phys. 24, 279–289 (2017). https://doi.org/10.1134/S1061920817030013

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  • DOI: https://doi.org/10.1134/S1061920817030013

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