The initial–boundary value problem for general non-local scalar conservation laws in one space dimension

We prove a global well-posedness result for a class of weak entropy solutions of bounded variation (BV) of scalar conservation laws with non-local flux on bounded domains, under suitable regularity assumptions on the flux function. In particular, existence is obtained by proving the convergence of an adapted Lax–Friedrichs algorithm. Lipschitz continuous dependence from initial and boundary data is derived applying Kružhkov’s doubling of variable technique.