We discuss a class of coupled system of nonlocal balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution is proven via doubling of the variables arguments and convergent finite volume approximations, respectively. The numerical approximations are proven to converge to the unique entropy solution of the system at the rate $\sqrt{\Delta t}$. The applicability of the proven theory to a general class of systems of nonlocal balance laws coupled strongly through the convective part and weakly through the source part, is also indicated. Numerical simulations illustrating the theory and the behavior of the entropy solution as the support of the kernel goes to zero(nonlocal to local limit), are shown.

翻译：我们讨论了一类描述多车道交通的非局部平衡定律耦合系统，其非局部性同时存在于对流项和源项中。通过变量对偶论证和收敛的有限体积逼近，分别证明了熵解的唯一性和存在性。数值逼近以 $\sqrt{\Delta t}$ 的收敛速率趋近于系统的唯一熵解。同时指出了所证理论对一类通过对流部分强耦合、通过源部分弱耦合的非局部平衡定律广义系统的适用性。文中展示了数值模拟，以阐释该理论以及核函数支撑趋于零时（非局部到局部极限）熵解的渐近行为。