We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J.Math.Anal 55.3 (2023)]" is the presence of a source term; this causes the solutions to no longer be probability measures, thus requiring a suitable adaptation of the numerical scheme and of the estimates leading to compactness.

翻译：本文研究一种确定性粒子格式，用于求解具有非局部相互作用和非线性迁移率的标量平衡方程，该方程常用于建模拥堵动力学。相较于"Radici-Stra [SIAM J.Math.Anal 55.3 (2023)]"的主要创新在于源项的存在：这导致解不再具有概率测度性质，因而需要对数值格式及紧致性估计进行相应调整。