Developments in the theory of the Prigogine-Herman kinetic equation of vehicular traffic
The nonlinear kinetic equation of Prigogine and Herman is examined in regards to existence and uniqueness of solutions. The solution exists and is unique in the Banach space of bounded continuous functions over a particular subspace Ω. The equilibrium solution of the kinetic equation of Prigogine and Herman is used to derive asymptotic type series expansions in the form of Hilbert or Chapman and