论文标题
重新审视汉堡的方程式：网络上单维情况的扩展
Burgers' equation revisited: extension of mono-dimensional case on a network
论文作者
论文摘要
本文介绍了无环公制图上汉堡方程的分析。主要目标是在$ TV $ - 规律性类别中建立弱解决方案的存在。关键点是遵守基尔霍夫法律的顶点的传播条件。首先，我们考虑在任意无环网络上的积极解决方案，并突出显示两种顶点，描述了顶点处的两种流动分裂机制。接下来，我们在顶点设计规则，用于为任何六角形网格的任何子图的任意标志解决方案，从而导致用$ tv $ $的通用解决方案的构建 - 该类别的网络规律性。引入的传输条件是由于能量估计的变化而动机。
The paper deals with the analysis of Burgers' equation on acyclic metric graphs. The main goal is to establish the existence of weak solutions in the $TV$ -- class of regularity. A key point is transmission conditions in vertices obeying the Kirchhoff law. First, we consider positive solutions at arbitrary acyclic networks and highlight two kinds of vertices, describing two mechanisms of flow splitting at the vertex. Next we design rules at vertices for solutions of arbitrary sign for any subgraph of hexagonal grid, which leads to a construction of general solutions with $TV$ -- regularity for this class of networks. Introduced transmission conditions are motivated by the change of the energy estimation.
