Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 69, Issue 6, Pages 1542-1558Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080731402
Keywords
interaction of elementary waves; vacuum state; Aw-Rascle model; Riemann problem; traffic flow; hyperbolic conservation laws
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Funding
- National Natural Science Foundation of China
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In this paper, we study the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle in [SIAM J. Appl. Math., 60 (2000), pp. 916-938]. The solutions are obtained constructively when the initial data are three piecewise constant states. In particular, a new wave SJ in which a shock wave S and a contact discontinuity J coincide with each other is obtained during the process of interaction. Moreover, by studying the limits of the solutions as the perturbed parameter e tends to zero, it can be found that the Riemann solutions are stable for such perturbations with the initial data.
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