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.
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