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.

中文翻译：

---

最简单装饰图上变速度波动方程的局部渐近解

我们在通过将射线粘合到三维欧几里得空间上获得的最简单装饰图上考虑一个可变速度波动方程，并在射线上具有局部初始条件。波动算子应该是自伴的，这意味着在胶合点有一些边界条件。我们使用Maslov正则算子的构造来描述问题的渐近解的主要部分。对于胶合点上所有可能的边界条件，都可获得结果。