In this paper we consider a family of scalar conservation laws defined on an oriented star shaped graph and we study their vanishing viscosity approximations subject to general matching conditions at the node. In particular, we prove the existence of converging subsequence and we show that the limit is a weak solution of the original problem.

中文翻译：

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节点上一般传输条件下星型图上的粘度消失

在本文中，我们考虑了在有向星状图上定义的一类标量守恒律，并研究了在节点的一般匹配条件下它们的消失粘度近似值。特别是，我们证明了收敛子序列的存在，并且证明了该极限是原始问题的弱解。