Entropy admissibility of the limit solution for a nonlocal model of traffic flow

We consider a conservation law model of traffic flow, where the velocity each car depends on weighted average density $\rho$ ahead. The averaging kernel is exponential type: $w_\varepsilon (s)=\varepsilon^{-1} e^{-s / \varepsilon}$. For any decreasing function $v$, we prove that, as $\varepsilon \to 0$, limit solutions to nonlocal equation coincides with unique entropy-admissible solution scalar $\rho_t + {(\rho v(\rho))}_x = 0$.