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

Published online by Cambridge University Press:  17 February 2009

C. V. Pao
Affiliation:
North Carolina State University, Raleigh, North Carolina 27607, U.S.A.
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

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