Error Estimates for Systems of Nonlocal Balance Laws Modeling Dense Multilane Vehicular Traffic (2312.16928v4)

Abstract: We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via doubling of the variables arguments and convergent finite volume approximations, respectively. The primary goal is to establish that the finite volume numerical approximations of the system converge to the unique entropy solution at a rate of $\sqrt{\Delta t}$, even when using relatively less regular one-sided kernels, compared to the globally smooth kernels analyzed in [Num. Math., 156(1):237-271, 2024] and [IMA J. Numer. Anal., 44(6):3354-3392, 2024].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 indicated. As the support of the kernel tends to zero, the convergence of the entropy solutions of the proposed model to its local counterparts [SIAM J. Math. Anal., 51: 3694-3713, 2019] is also discussed. Numerical simulations illustrating the behavior of the entropy solutions of the coupled nonlocal systems are also shown.