Michael Herty - RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen, Germany (email)
Abstract: From a Vlasov-type kinetic equation with nonlocal braking and acceleration forces, taken as a traffic model for higher densities, we derive macroscopic equations generalizing the second order model of conservation laws suggested by Aw and Rascle  and Zhang . The nonlocality remains present in these equations, but more conventional, local equations are derived by using suitable Taylor expansion. A second order model of this type is discussed in some detail and is shown to possess traveling wave solutions that resemble stop-and-go waves in dense traffic. A phase space analysis suggests that inside the class of such traveling waves there are steady solutions that are stable.
Keywords: traffic flow,
stop-and-go waves, nonlinear stability, nonlocal equations.
Received: April 2008; Revised: May 2008; Published: August 2008.
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