论文标题
有限星状网络上线性传输方程的消失粘度近似
Vanishing viscosity approximation for linear transport equations on finite starshaped networks
论文作者
论文摘要
在本文中，我们研究了有限的面向星形网络上的线性抛物线方程。方程与内部节点设置的传输条件相结合，该节点不会在未知数上施加连续性。我们将这个问题视为网络上一组线性传输方程组的抛物线近似，我们证明，当扩散系数消失时，解决方案家族会收敛到一阶方程的唯一解决方案，并满足内部节点的合适传输条件，这取决于在寄生虫传输条件中出现的参数确定的。
In this paper we study linear parabolic equations on a finite oriented starshaped network; the equations are coupled by transmission conditions set at the inner node, which do not impose continuity on the unknown. We consider this problem as a parabolic approximation of a set of first order linear transport equations on the network and we prove that, when the diffusion coefficient vanishes, the family of solutions converges to the unique solution to the first order equations and satisfies suitable transmission conditions at the inner node, which are determined by the parameters appearing in the parabolic transmission conditions.
