Abstract A variable-velocity wave equation is studied on the simplest decorated graph, i.e., the topological space obtained by attaching a ray to $$\mathbb R^3$$ . The Cauchy problem with initial conditions localized on Euclidean space is considered. The leading term of an asymptotic solution of the problem under consideration as the parameter characterizing the size of the source tends to zero is described by using the construction of the Maslov canonical operator. It is assumed that the point on $$\mathbb R^3$$ at which the ray is attached is not a singular point of the wavefront.

中文翻译：

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带初始条件的最简单装饰图上变速度波动方程的局部渐近解

摘要 在最简单的装饰图上研究了变速波动方程，即在$$\mathbb R^3$$ 上附加一条射线所得到的拓扑空间。考虑了初始条件定位在欧几里得空间上的柯西问题。当表征源大小的参数趋于零时，所考虑问题的渐近解的前导项是通过使用 Maslov 规范算子的构造来描述的。假设射线附着在 $$\mathbb R^3$$ 上的点不是波前的奇异点。