In this note,we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved.The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states.Furthermore,it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.
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Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China School of Mathematical and Information, Ludong University, Yantai 264025, China;