Critical Thresholds in a Relaxation System with Resonance of Characteristic Speeds
نویسندگان
چکیده
We study critical threshold phenomena in a dynamic continuum traffic flow model known as the Payne and Whitham (PW) model. This model is a quasi-linear hyperbolic relaxation system, and when equilibrium velocity is specifically associated with pressure, the equilibrium characteristic speed resonates with one characteristic speed of the full relaxation system. For a scenario of physical interest we identify a lower threshold for finite time singularity in solutions and an upper threshold for the global existence of the smooth solution. The set of initial data leading to global smooth solutions is large, in particular allowing initial velocity of negative slope.
منابع مشابه
Critical Thresholds in Relaxation Systems with Resonance of Characteristic Speeds
In this paper, we consider hyperbolic relaxation systems arising from dynamic continuum traffic flow models including the well-known Payne and Whitham (PW) model. The equilibrium characteristic speed resonates with one characteristic speed of the full relaxation system in many physical scenarios in traffic flow, for which the usual subcharacteristic condition only marginally holds. In spite of ...
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