# American Institute of Mathematical Sciences

December  2006, 1(4): 601-619. doi: 10.3934/nhm.2006.1.601

## On the variational theory of traffic flow: well-posedness, duality and applications

 1 Department of Civil and Environmental Engineering, 416 McLaughlin Hall, Berkeley, CA 94707, United States

Received  July 2006 Revised  September 2006 Published  October 2006

This paper describes some simplifications allowed by the variational theory of traffic flow(VT). It presents general conditions guaranteeing that the solution of a VT problem with bottlenecks exists, is unique and makes physical sense; i.e., that the problem is well-posed. The requirements for well-posedness are mild and met by practical applications. They are consistent with narrower results available for kinematic wave or Hamilton-Jacobi theories. The paper also describes some duality ideas relevant to these theories. Duality and VT are used to establish the equivalence of eight traffic models. Finally, the paper discusses how its ideas can be used to model networks of multi-lane traffic streams.
Citation: Carlos F. Daganzo. On the variational theory of traffic flow: well-posedness, duality and applications. Networks & Heterogeneous Media, 2006, 1 (4) : 601-619. doi: 10.3934/nhm.2006.1.601
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