  We study a class of nonlinear nonlocal conservation laws with discontinuous
flux, modeling crowd dynamics and traffic flow, without any additional
conditions on finiteness/discreteness of the set of discontinuities or on the
monotonicity of the kernel/the discontinuous coefficient. Strong compactness of
the Godunov and Lax-Friedrichs type approximations is proved, providing the
existence of entropy solutions. A proof of the uniqueness of the adapted
entropy solutions is provided, establishing the convergence of the entire
sequence of finite volume approximations to the adapted entropy solution. As
per the current literature, this is the first well-posedness result for the
aforesaid class and connects the theory of nonlocal conservation laws (with
discontinuous flux), with its local counterpart in a generic setup. Some
numerical examples are presented to display the performance of the schemes and
explore the limiting behavior of these nonlocal conservation laws to their
local counterparts.
