IBVPs for scalar conservation laws with time discontinuous fluxes

The initial boundary value problem for a class of scalar nonautonomous conservation laws in 1 space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity assumptions on the flow are extended to a merely L∞ dependence on time. These results ensure, for instance, the well‐posedness of a class of vehicular traffic models with time‐dependent speed limits. A traffic management problem is then shown to admit an optimal solution.