A space-time nonlocal traffic flow model: Relaxation representation and local limit

We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that information travels at finite speed model involves space-time integral weighted density. The well-posedness established under suitable conditions on parameters by suitably-defined initial condition. In special case where weight kernel an exponential function, can be reformulated as $2\times2$ hyperbolic system with relaxation. With help this relaxation representation, we show Lighthill-Whitham-Richards recovered equilibrium approximation limit.