Transport of measures on networks
Transport of measures on networks
复制标题
网络上的措施传输
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
A. Tosin
中科院分区：
文献类型：
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作者：
F. Camilli;Raul De Maio;A. Tosin
本文给出了网络上测度值线性迁移方程的一个理论。我们的方法的基石是有界区间上的测度值线性迁移方程的初边值问题，这是一个弧的网络的原型。对于这个问题，我们给出了一个明确的表示公式的解决方案，它也考虑了总质量流出的区间。然后，我们构造的整体解决方案的网络上的所有测量值的解决方案，通过粘合的弧适当的分布规则在顶点。测度值方法使我们的框架适合于处理网络上的多尺度流，微观和宏观阶段分别由Lebesgue奇异和Lebesgue绝对连续测度在时间和空间上表示。
In this paper we formulate a theory of measure-valued linear transport equations on networks. The building block of our approach is the initial and boundary-value problem for the measure-valued linear transport equation on a bounded interval, which is the prototype of an arc of the network. For this problem we give an explicit representation formula of the solution, which also considers the total mass flowing out of the interval. Then we construct the global solution on the network by gluing all the measure-valued solutions on the arcs by means of appropriate distribution rules at the vertexes. The measure-valued approach makes our framework suitable to deal with multiscale flows on networks, with the microscopic and macroscopic phases represented by Lebesgue-singular and Lebesgue-absolutely continuous measures, respectively, in time and space.