Geodesic
Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 265-275.

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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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A. V. Tsvetkova; A. I. Shafarevich. Localized Asymptotic Solution of a Variable-Velocity Wave Equation on the Simplest Decorated Graph. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 308 (2020), pp. 265-275. http://geodesic.mathdoc.fr/item/TM_2020_308_a19/

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