We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity coefficients, the corresponding non-autonomous abstract Cauchy problem is well-posed by means of evolution families and evolution semigroups.

中文翻译：

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度量图上非自治输运方程的适定性

我们考虑具有时间相关速度的度量图上的传输过程，并表明，在速度系数的连续性假设下，相应的非自治抽象柯西问题通过演化族和演化半群得到适定。