Abstract :

This talk focuses on scalar and systems of nonlocal conservation laws and their applications in modeling traffic dynamics. The key objectives of the talk are threefold: 1. Establishing the existence of an entropy solution by deriving a uniform total variation (TV) bound on finite-volume approximations. 2. Deriving a novel Kuznetsov-type lemma, thereby proving the uniqueness of the entropy solution. 3. Proving the convergence rate of the finite-volume approximations to the entropy solution as 1/2. We will also present numerical experiments to illustrate the convergence rates.