Abstract We discuss a class of coupled systems of nonlocal nonlinear balance laws modelling 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 Δ t , even when using relatively less regular one-sided kernels, compared to the globally smooth kernels analysed in Aggarwal et al (2024 Num. Math. 156 237–71) and Aggarwal et al (2024 IMA J. Numer. Anal. 44 3354–92). 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 (Holden and Risebro 2019 SIAM J. Math. Anal. 51 3694–3713) is also discussed. Numerical simulations illustrating the behaviour of the entropy solutions of the coupled nonlocal systems are also shown.
Aggarwal et al. (Fri,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: