Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways

Abstract

In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation