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.
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This work is supported by the Russian Science Foundation under grant 16-11-10069.
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Russian Text © The Author(s), 2020, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 265–275.
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Tsvetkova, A.V., Shafarevich, A.I. Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph. Proc. Steklov Inst. Math. 308, 250–260 (2020). https://doi.org/10.1134/S0081543820010204
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DOI: https://doi.org/10.1134/S0081543820010204