A Well Posed Conservation Law with a Variable Unilateral Constraint

This paper considers the Cauchy problem for a conservation
law with a variable unilateral constraint, its motivation being, for
instance, the modeling of a toll gate along a highway. This problem is
solved by means of nonclassical shocks and its well posedness is
proved. Then, the solutions so obtained are shown to coincide with the
limits of the classical solutions to suitable conservation laws with
discontinuous flux function that approximate the constrained problem.