Well-posedness theory of an inhomogeneous traffic flow model

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August 2002, 2(3): 401-414. doi: 10.3934/dcdsb.2002.2.401

Well-posedness theory of an inhomogeneous traffic flow model

1.	Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, United States

Received August 2001 Revised December 2001 Published May 2002

Abstract
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We study a traffic flow model with inhomogeneous road conditions such as obstacles. The model is a system of nonlinear hyperbolic equations with both relaxation and sources. The flux and the source terms depend on the space variable. Waves for such a system propagate in a more complicated way than those do for models with homogeneous road conditions.
The $L^1$ well-posedness theory for the model is established. In particular, we derive the continuous dependence of the solution on its initial data in $L^1$ topology. Moreover, the $L^1$-convergence to the unique zero relaxation limit is proved. Finally, the asymptotic states of a general solution whose initial data tend to constant states as $|x| \rightarrow +\infty$ are constructed.

Keywords: $L^1$-contraction, Inhomogeneous, marginally stable, zero relaxation limit..

Mathematics Subject Classification: 35B30, 35B50, 35L65, 76H0.

Citation: Tong Li. Well-posedness theory of an inhomogeneous traffic flow model. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 401-414. doi: 10.3934/dcdsb.2002.2.401

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