  We investigate a class of nonlocal conservation laws in several space
dimensions, where the continuum average of weighted nonlocal interactions are
considered over a finite horizon. We establish well-posedness for a broad class
of flux functions and initial data via semigroup theory in Banach spaces and,
in particular, via the celebrated Crandall-Liggett Theorem. We also show that
the unique mild solution satisfies a Kru\v{z}kov-type nonlocal entropy
inequality. Similarly to the local case, we demonstrate an efficient way of
proving various desirable qualitative properties of the unique solution.
