Vanishing viscosity approximation for linear transport equations on finite star-shaped networks
Vanishing viscosity approximation for linear transport equations on finite star-shaped networks
复制标题
有限星形网络上线性输运方程的消失粘度近似
DOI：
10.1007/s00028-021-00688-0
复制
发表时间：
2020
影响因子：
1.4
通讯作者：
R. Natalini
中科院分区：
文献类型：
--
作者：
F. R. Guarguaglini;R. Natalini
本文研究了有限定向星形网络上的线性抛物型方程，方程通过设置在内节点的传输条件耦合，该条件不对未知量施加连续性。我们把这个问题看作是网络上一组一阶线性输运方程的抛物近似，并证明了当扩散系数为零时，解族收敛于一阶方程的唯一解，该解满足适当的内节点处的传输条件，而传输条件由抛物传输条件中出现的参数决定.
In this paper, we study linear parabolic equations on a finite oriented star-shaped 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 the 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 satisfying suitable transmission conditions at the inner node, which are determined by the parameters appearing in the parabolic transmission conditions.