The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

A Boltzmann-type equation in the kinetic theory of vehicular traffic

C. V. Paoa1

a1 North Carolina State University, Raleigh, North Carolina 27607, U.S.A.

Abstract

In the theory of vehicular traffic flow on a highway the traffic interaction process is often considered as a collision similar to the particles' interaction in the kinetic theory of gases. This concept leads to a Boltzmann-type nonlinear intergro-differential equation which governs the traffic density function. The purpose of this paper is to present a constructive method for the determintation of a solution for this type of equation under certain boundary and initial conditions. Our method is by successive approximation which yields existence of both global and local solutions of the problem.

(Received December 11 1975)

(Revised June 30 1976)