Special Session 37: 

Thresholds for shock formation in a class of non-local conservation laws with concavity changing flux

Yongki Lee
Georgia Southern University
USA
Co-Author(s):    
Abstract:
We identify sub-thresholds for finite time shock formation in a class of non-local conservation law with concavity changing flux. From a class of non-local conservation laws, the Riccati-type ODE system that governs a solution`s gradient is obtained. The changes in concavity of the flux function correspond to the sign changes in the leading coefficient functions of the ODE system. We identify the blow-up condition of this structurally generalized Riccati-type ODE. The method is illustrated via the Whitham-type equation and the traffic flow models with nonlocal-concave-convex flux.