Highway traffic flow discontinuous functions of dynamic mathematical model and solution in their class

A mathematical model reflecting properly the dynamics of traffic flow on highways has been constructed. In the case of , the solution is observed as a piecewise continuous function, where and are the densities of cars on the left and right side of the intersection respectively. On the contrary case, it has been proven that a shock of which the location is unknown beforehand arises in the solution and furthermore a method specifying the location of jump has also been proposed. In addition to the realization of the suggested method, the parameters of the flow are also found.