Critical Thresholds in Relaxation Systems

Tong Li

Department of Mathematics
University of Iowa

In this talk, 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 this obstacle, we prove global in time regularity and finite time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the underlying relaxation systems. This is a joint work with Hailiang Liu.