Systems of nonlocal balance laws For Dense multilane vehicular traffic

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.