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.
